A jar contains only Rs. 5 and Rs. 10 coins. There are 69 coins with a total value of Rs. 405. How many Rs. 10 coins are there?
Medium
ExplanationLet x = Rs.5 coins, y = Rs.10 coins. x + y = 69 and 5x + 10y = 405. Solving gives x = 57, y = 12.
2
A line has slope 5/9 and passes through (27, -13). What is its y-intercept?
Medium
ExplanationUsing y = mx + b: -13 = (5/9)(27) + b, so b = -13 − 15 = -28.
3
If -8x + 9y = -31 and 5x + 4y = -48, what is x + y?
Medium
ExplanationSolving the system gives x = -4 and y = -7, so x + y = -11.
4
Solve the system for y: 4x + 6y = 66, 9x − 6y = -66
Medium
ExplanationSolving the system by elimination or substitution gives y = 11 (and x = 0).
5
What is the value of -2x − 7 when x = 15?
Medium
Explanation-2(15) − 7 = -30 − 7 = -37.
6
A delivery service charges a fixed fee of Rs. 44 plus Rs. 24 per item. If a customer has a budget of Rs. 650, what is the maximum number of items they can order?
Medium
Explanation44 + 24n ≤ 650, so n ≤ 606/24 ≈ 25.25, meaning at most 25 items.
7
Solve for x: 10x − 2 < 208
Medium
Explanation10x < 208 − (-2) = 210, so x < 21.
8
A cinema sells adult tickets for Rs. 27 and child tickets for Rs. 24. If 53 tickets were sold for a total of Rs. 1305, how many adult tickets were sold?
Medium
ExplanationLet a = adult tickets, c = child tickets. a + c = 53 and 27a + 24c = 1305. Solving gives a = 11, c = 42.
9
A delivery service charges a fixed fee of Rs. 48 plus Rs. 39 per item. If a customer has a budget of Rs. 714, what is the maximum number of items they can order?
Medium
Explanation48 + 39n ≤ 714, so n ≤ 666/39 ≈ 17.08, meaning at most 17 items.
10
Solve for x: -4x + 0 = -7x + 75
Medium
ExplanationMoving variable terms to one side: (-4−-7)x = 75−(0), so x = (75)/(3) = 25.
— Sponsored —
11
Solve for x: 3x − 13 = -8x + 119
Medium
ExplanationMoving variable terms to one side: (3−-8)x = 119−(-13), so x = (132)/(11) = 12.
12
Solve for x: -7x + 30 < -19
Medium
ExplanationDividing both sides by the negative coefficient -7 reverses the inequality sign, giving x > 7.
13
A cinema sells adult tickets for Rs. 12 and child tickets for Rs. 7. If 20 tickets were sold for a total of Rs. 220, how many adult tickets were sold?
Medium
ExplanationLet a = adult tickets, c = child tickets. a + c = 20 and 12a + 7c = 220. Solving gives a = 16, c = 4.
14
A jar contains only Rs. 5 and Rs. 10 coins. There are 53 coins with a total value of Rs. 300. How many Rs. 10 coins are there?
Medium
ExplanationLet x = Rs.5 coins, y = Rs.10 coins. x + y = 53 and 5x + 10y = 300. Solving gives x = 46, y = 7.
15
A jar contains only Rs. 5 and Rs. 10 coins. There are 70 coins with a total value of Rs. 590. How many Rs. 10 coins are there?
Medium
ExplanationLet x = Rs.5 coins, y = Rs.10 coins. x + y = 70 and 5x + 10y = 590. Solving gives x = 22, y = 48.
16
A jar contains only Rs. 5 and Rs. 10 coins. There are 109 coins with a total value of Rs. 820. How many Rs. 10 coins are there?
Medium
ExplanationLet x = Rs.5 coins, y = Rs.10 coins. x + y = 109 and 5x + 10y = 820. Solving gives x = 54, y = 55.
17
A cinema sells adult tickets for Rs. 16 and child tickets for Rs. 13. If 74 tickets were sold for a total of Rs. 1097, how many adult tickets were sold?
Medium
ExplanationLet a = adult tickets, c = child tickets. a + c = 74 and 16a + 13c = 1097. Solving gives a = 45, c = 29.
18
What is the value of -11x − 7 when x = 10?
Medium
Explanation-11(10) − 7 = -110 − 7 = -117.
19
Solve the system for y: -6x − 8y = 48, 2x + 7y = -81
Medium
ExplanationSolving the system by elimination or substitution gives y = -15 (and x = 12).
20
Given 6x + 10y = -10, what is y when x = 30?
Medium
Explanation10y = -10 − 6(30) = -10 − 180 = -190, so y = -190/10 = -19.
— Sponsored —
21
Solve for x: 12x − 7 = -3x + 278
Medium
ExplanationMoving variable terms to one side: (12−-3)x = 278−(-7), so x = (285)/(15) = 19.
22
What is the x-intercept of the line 8x + 10y = -64?
Medium
ExplanationSet y = 0: 8x = -64, so x = -64/8 = -8.
23
Solve for x: -9 < 8x + 7 < 47
Medium
ExplanationSubtracting 7 from all parts: -16 < 8x < 40. Dividing by 8: -2 < x < 5.
24
How many solutions does the equation 3x + 5 = 12x + 17 have?
Medium
ExplanationSince the coefficients of x differ, the equation has exactly one solution.
25
Solve for x: 4(x − 3) = -24
Medium
ExplanationDividing both sides by 4: x − 3 = -6, so x = -3.
26
How many solutions does the equation 9x + 14 = 9x + 14 have?
Medium
ExplanationBoth sides are identical for every x, so every value of x works — infinitely many solutions.
27
What is the slope of the line through (0, -17) and (3, -27)?
ExplanationDividing both sides by 6: x − 20 = -41, so x = -21.
29
What is the y-intercept of the line 4x + 4y = -20?
Medium
ExplanationSet x = 0: 4y = -20, so y = -20/4 = -5.
30
What is the x-intercept of the line 4x + 12y = 20?
Medium
ExplanationSet y = 0: 4x = 20, so x = 20/4 = 5.
— Sponsored —
31
A jar contains only Rs. 5 and Rs. 10 coins. There are 66 coins with a total value of Rs. 510. How many Rs. 10 coins are there?
Medium
ExplanationLet x = Rs.5 coins, y = Rs.10 coins. x + y = 66 and 5x + 10y = 510. Solving gives x = 30, y = 36.
32
Solve for x: 2x − 20 = x − 32
Medium
ExplanationMoving variable terms to one side: (2−1)x = -32−(-20), so x = (-12)/(1) = -12.
33
A cinema sells adult tickets for Rs. 28 and child tickets for Rs. 19. If 38 tickets were sold for a total of Rs. 848, how many adult tickets were sold?
Medium
ExplanationLet a = adult tickets, c = child tickets. a + c = 38 and 28a + 19c = 848. Solving gives a = 14, c = 24.
34
What is the value of -5x − 24 when x = 8?
Medium
Explanation-5(8) − 24 = -40 − 24 = -64.
35
Solve for x: -13x − 14 > 38
Medium
ExplanationDividing both sides by the negative coefficient -13 reverses the inequality sign, giving x < -4.
36
Solve for x: -59 < 3x − 5 < -26
Medium
ExplanationSubtracting -5 from all parts: -54 < 3x < -21. Dividing by 3: -18 < x < -7.
37
Solve for x: -12x − 18 = 6x + 198
Medium
ExplanationMoving variable terms to one side: (-12−6)x = 198−(-18), so x = (216)/(-18) = -12.
38
Solve for x: -2(x + 14) = -2
Medium
ExplanationDividing both sides by -2: x + 14 = 1, so x = -13.
39
If -5x + 2y = 64 and 9x − 3y = -123, what is x + y?
Medium
ExplanationSolving the system gives x = -18 and y = -13, so x + y = -31.
40
Solve for x: 7x + 3 ≥ -60
Medium
Explanation7x ≥ -60 − (3) = -63, so x ≥ -9.
— Sponsored —
41
What is the slope of the line through (-5, 15) and (-13, -5)?
A delivery service charges a fixed fee of Rs. 15 plus Rs. 23 per item. If a customer has a budget of Rs. 419, what is the maximum number of items they can order?
Medium
Explanation15 + 23n ≤ 419, so n ≤ 404/23 ≈ 17.57, meaning at most 17 items.
43
What is the y-intercept of the line 14x + 3y = -36?
Medium
ExplanationSet x = 0: 3y = -36, so y = -36/3 = -12.
44
Solve for x: -3x − 22 < -13
Medium
ExplanationDividing both sides by the negative coefficient -3 reverses the inequality sign, giving x > -3.
45
How many solutions does the equation 8x + 8 = 8x + 16 have?
Medium
ExplanationThe x-terms cancel leaving a false statement (since 8 ≠ 16), so there is no solution.
46
A jar contains only Rs. 5 and Rs. 10 coins. There are 105 coins with a total value of Rs. 795. How many Rs. 10 coins are there?
Medium
ExplanationLet x = Rs.5 coins, y = Rs.10 coins. x + y = 105 and 5x + 10y = 795. Solving gives x = 51, y = 54.
47
Solve for x: -5x + 23 < 103
Medium
ExplanationDividing both sides by the negative coefficient -5 reverses the inequality sign, giving x > -16.
48
Solve for x: (x + 15) = -4(x + 15)
Medium
ExplanationExpanding both sides and collecting x terms gives x = -15.
49
What is the y-intercept of the line 13x + 7y = 14?
Medium
ExplanationSet x = 0: 7y = 14, so y = 14/7 = 2.
50
Solve for x: -3(x − 20) = 63
Medium
ExplanationDividing both sides by -3: x − 20 = -21, so x = -1.
— Sponsored —
51
If -9x − 4y = 59 and -7x + 7y = 238, what is x + y?
Medium
ExplanationSolving the system gives x = -15 and y = 19, so x + y = 4.
52
Solve for x: 14x + 15 ≥ -69
Medium
Explanation14x ≥ -69 − (15) = -84, so x ≥ -6.
53
Solve for x: -5(x − 16) = -35
Medium
ExplanationDividing both sides by -5: x − 16 = 7, so x = 23.
54
Solve for x: -4x + 23 = 123
Medium
Explanation-4x = 123 − (23) = 100, so x = 100/-4 = -25.
55
A cinema sells adult tickets for Rs. 5 and child tickets for Rs. 3. If 37 tickets were sold for a total of Rs. 181, how many adult tickets were sold?
Medium
ExplanationLet a = adult tickets, c = child tickets. a + c = 37 and 5a + 3c = 181. Solving gives a = 35, c = 2.
56
A delivery service charges a fixed fee of Rs. 32 plus Rs. 24 per item. If a customer has a budget of Rs. 385, what is the maximum number of items they can order?
Medium
Explanation32 + 24n ≤ 385, so n ≤ 353/24 ≈ 14.71, meaning at most 14 items.
57
If 8x − 5y = -75 and -x − 9y = 173, what is x + y?
Medium
ExplanationSolving the system gives x = -20 and y = -17, so x + y = -37.
58
How many solutions does the equation 12x + -19 = 12x + -12 have?
Medium
ExplanationThe x-terms cancel leaving a false statement (since -19 ≠ -12), so there is no solution.
59
Solve the system for y: -9x + 4y = -103, -9x + 2y = -83
Medium
ExplanationSolving the system by elimination or substitution gives y = -10 (and x = 7).
60
Solve for x: 2x − 27 ≥ -1
Medium
Explanation2x ≥ -1 − (-27) = 26, so x ≥ 13.
— Sponsored —
61
Solve for x: 12x − 35 = -287
Medium
Explanation12x = -287 − (-35) = -252, so x = -252/12 = -21.
62
Solve for x: 2x − 2 < 0
Medium
Explanation2x < 0 − (-2) = 2, so x < 1.
63
What is the y-intercept of the line 14x + 9y = 72?
Medium
ExplanationSet x = 0: 9y = 72, so y = 72/9 = 8.
64
A jar contains only Rs. 5 and Rs. 10 coins. There are 53 coins with a total value of Rs. 425. How many Rs. 10 coins are there?
Medium
ExplanationLet x = Rs.5 coins, y = Rs.10 coins. x + y = 53 and 5x + 10y = 425. Solving gives x = 21, y = 32.
65
A jar contains only Rs. 5 and Rs. 10 coins. There are 104 coins with a total value of Rs. 800. How many Rs. 10 coins are there?
Medium
ExplanationLet x = Rs.5 coins, y = Rs.10 coins. x + y = 104 and 5x + 10y = 800. Solving gives x = 48, y = 56.
66
A jar contains only Rs. 5 and Rs. 10 coins. There are 76 coins with a total value of Rs. 535. How many Rs. 10 coins are there?
Medium
ExplanationLet x = Rs.5 coins, y = Rs.10 coins. x + y = 76 and 5x + 10y = 535. Solving gives x = 45, y = 31.
67
Solve for x: 13x − 3 < -81
Medium
Explanation13x < -81 − (-3) = -78, so x < -6.
68
Solve for x: -5x + 1 = 7x + 169
Medium
ExplanationMoving variable terms to one side: (-5−7)x = 169−(1), so x = (168)/(-12) = -14.
69
Solve for x: 116 < 10x + 6 < 196
Medium
ExplanationSubtracting 6 from all parts: 110 < 10x < 190. Dividing by 10: 11 < x < 19.
70
Solve for x: -1 < x + 17 < 12
Medium
ExplanationSubtracting 17 from all parts: -18 < 1x < -5. Dividing by 1: -18 < x < -5.
— Sponsored —
71
What is the x-intercept of the line 9x + 7y = 18?
Medium
ExplanationSet y = 0: 9x = 18, so x = 18/9 = 2.
72
Solve for x: 12x + 27 = 207
Medium
Explanation12x = 207 − (27) = 180, so x = 180/12 = 15.
73
Solve for x: x − 10 > -6
Medium
Explanationx > -6 − (-10) = 4, so x > 4.
74
Solve the system for x: -x + 8y = 55, 8x + 2y = -110
Medium
ExplanationSolving the system by elimination or substitution gives x = -15 (and y = 5).
75
A cinema sells adult tickets for Rs. 16 and child tickets for Rs. 5. If 96 tickets were sold for a total of Rs. 1085, how many adult tickets were sold?
Medium
ExplanationLet a = adult tickets, c = child tickets. a + c = 96 and 16a + 5c = 1085. Solving gives a = 55, c = 41.
76
Solve for x: -104 < 6x − 14 < -26
Medium
ExplanationSubtracting -14 from all parts: -90 < 6x < -12. Dividing by 6: -15 < x < -2.
77
Solve for x: 55 < 9x − 8 < 127
Medium
ExplanationSubtracting -8 from all parts: 63 < 9x < 135. Dividing by 9: 7 < x < 15.
78
How many solutions does the equation 6x + -15 = 7x + -2 have?
Medium
ExplanationSince the coefficients of x differ, the equation has exactly one solution.
79
Solve for x: -11x + 22 = -275
Medium
Explanation-11x = -275 − (22) = -297, so x = -297/-11 = 27.
80
Solve for x: 7(x − 20) = -28
Medium
ExplanationDividing both sides by 7: x − 20 = -4, so x = 16.
— Sponsored —
81
Solve for x: -9x − 9 = -198
Medium
Explanation-9x = -198 − (-9) = -189, so x = -189/-9 = 21.
82
Solve the system for y: 9x − 3y = -90, 4x − 3y = -50
Medium
ExplanationSolving the system by elimination or substitution gives y = 6 (and x = -8).
83
Solve the system for x: 6x − 7y = -80, -7x + 6y = 89
Medium
ExplanationSolving the system by elimination or substitution gives x = -11 (and y = 2).
84
Solve the system for y: -8x + y = 95, -2x − 4y = -40
Medium
ExplanationSolving the system by elimination or substitution gives y = 15 (and x = -10).
85
If x + 5y = 26 and -5x − 4y = -46, what is x + y?
Medium
ExplanationSolving the system gives x = 6 and y = 4, so x + y = 10.
86
Solve for x: -11x + 22 > 176
Medium
ExplanationDividing both sides by the negative coefficient -11 reverses the inequality sign, giving x < -14.
87
Solve the system for x: -2x − 4y = 6, x + 9y = 18
Medium
ExplanationSolving the system by elimination or substitution gives x = -9 (and y = 3).
88
What is the slope of the line through (16, 9) and (26, 15)?