A delivery service charges a fixed fee of Rs. 37 plus Rs. 11 per item. If a customer has a budget of Rs. 103, what is the maximum number of items they can order?
Medium
Explanation37 + 11n ≤ 103, so n ≤ 66/11 ≈ 6.00, meaning at most 6 items.
2
A cinema sells adult tickets for Rs. 7 and child tickets for Rs. 3. If 68 tickets were sold for a total of Rs. 424, how many adult tickets were sold?
Medium
ExplanationLet a = adult tickets, c = child tickets. a + c = 68 and 7a + 3c = 424. Solving gives a = 55, c = 13.
3
Solve for x: -11x + 30 > -69
Medium
ExplanationDividing both sides by the negative coefficient -11 reverses the inequality sign, giving x < 9.
4
Solve for x: -17 < x + 2 < -13
Medium
ExplanationSubtracting 2 from all parts: -19 < 1x < -15. Dividing by 1: -19 < x < -15.
5
What is the slope of the line through (-11, -1) and (-21, -3)?
A delivery service charges a fixed fee of Rs. 33 plus Rs. 5 per item. If a customer has a budget of Rs. 177, what is the maximum number of items they can order?
Medium
Explanation33 + 5n ≤ 177, so n ≤ 144/5 ≈ 28.80, meaning at most 28 items.
8
A delivery service charges a fixed fee of Rs. 28 plus Rs. 21 per item. If a customer has a budget of Rs. 481, what is the maximum number of items they can order?
Medium
Explanation28 + 21n ≤ 481, so n ≤ 453/21 ≈ 21.57, meaning at most 21 items.
9
Solve for x: 103 < 7x + 12 < 131
Medium
ExplanationSubtracting 12 from all parts: 91 < 7x < 119. Dividing by 7: 13 < x < 17.
10
What is the x-intercept of the line 7x + 8y = -56?
Medium
ExplanationSet y = 0: 7x = -56, so x = -56/7 = -8.
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11
A cinema sells adult tickets for Rs. 18 and child tickets for Rs. 17. If 87 tickets were sold for a total of Rs. 1534, how many adult tickets were sold?
Medium
ExplanationLet a = adult tickets, c = child tickets. a + c = 87 and 18a + 17c = 1534. Solving gives a = 55, c = 32.
12
What is the x-intercept of the line 11x + 3y = 33?
Medium
ExplanationSet y = 0: 11x = 33, so x = 33/11 = 3.
13
If -4x + 9y = 124 and x + 3y = 53, what is x + y?
Medium
ExplanationSolving the system gives x = 5 and y = 16, so x + y = 21.
14
Solve for x: x/4 + x/5 = -45
Medium
ExplanationCombining terms: x(1/4 + 1/5) = -45, so x × (9)/20 = -45, giving x = -100.
15
Solve the system for y: -8x + 4y = 0, 3x − 5y = -35
Medium
ExplanationSolving the system by elimination or substitution gives y = 10 (and x = 5).
16
Solve for x: 4x + 7 = 12x + 71
Medium
ExplanationMoving variable terms to one side: (4−12)x = 71−(7), so x = (64)/(-8) = -8.
17
Solve for x: -2(x + 14) = -34
Medium
ExplanationDividing both sides by -2: x + 14 = 17, so x = 3.
18
What is the slope of the line through (-1, -3) and (-2, -13)?
Explanation-6x = 103 − (-5) = 108, so x = 108/-6 = -18.
20
How many solutions does the equation 10x + -1 = 10x + 4 have?
Medium
ExplanationThe x-terms cancel leaving a false statement (since -1 ≠ 4), so there is no solution.
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21
How many solutions does the equation 2x + -19 = 7x + 7 have?
Medium
ExplanationSince the coefficients of x differ, the equation has exactly one solution.
22
If -5x + 4y = 137 and 4x − 6y = -160, what is x + y?
Medium
ExplanationSolving the system gives x = -13 and y = 18, so x + y = 5.
23
Solve for x: -5(x − 16) = 130
Medium
ExplanationDividing both sides by -5: x − 16 = -26, so x = -10.
24
Solve for x: 7(x − 5) = 84
Medium
ExplanationDividing both sides by 7: x − 5 = 12, so x = 17.
25
Solve for x: -108 < 7x + 18 < -59
Medium
ExplanationSubtracting 18 from all parts: -126 < 7x < -77. Dividing by 7: -18 < x < -11.
26
What is the value of 12x − 14 when x = 17?
Medium
Explanation12(17) − 14 = 204 − 14 = 190.
27
What is the value of 5x − 11 when x = -12?
Medium
Explanation5(-12) − 11 = -60 − 11 = -71.
28
A line has slope -4/3 and passes through (6, -17). What is its y-intercept?
Medium
ExplanationUsing y = mx + b: -17 = (-4/3)(6) + b, so b = -17 − -8 = -9.
29
A jar contains only Rs. 5 and Rs. 10 coins. There are 106 coins with a total value of Rs. 785. How many Rs. 10 coins are there?
Medium
ExplanationLet x = Rs.5 coins, y = Rs.10 coins. x + y = 106 and 5x + 10y = 785. Solving gives x = 55, y = 51.
30
Solve for x: x/11 + x/8 = -38
Medium
ExplanationCombining terms: x(1/11 + 1/8) = -38, so x × (19)/88 = -38, giving x = -176.
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31
Solve the system for y: -5x + 4y = 34, 4x + 8y = 152
Medium
ExplanationSolving the system by elimination or substitution gives y = 16 (and x = 6).
32
Solve for x: -4x − 23 = -6x + 11
Medium
ExplanationMoving variable terms to one side: (-4−-6)x = 11−(-23), so x = (34)/(2) = 17.
33
A delivery service charges a fixed fee of Rs. 44 plus Rs. 25 per item. If a customer has a budget of Rs. 786, what is the maximum number of items they can order?
Medium
Explanation44 + 25n ≤ 786, so n ≤ 742/25 ≈ 29.68, meaning at most 29 items.
34
A jar contains only Rs. 5 and Rs. 10 coins. There are 49 coins with a total value of Rs. 440. How many Rs. 10 coins are there?
Medium
ExplanationLet x = Rs.5 coins, y = Rs.10 coins. x + y = 49 and 5x + 10y = 440. Solving gives x = 10, y = 39.
35
What is the y-intercept of the line 6x + 6y = 36?
Medium
ExplanationSet x = 0: 6y = 36, so y = 36/6 = 6.
36
Solve for x: x + 32 = 39
Medium
Explanationx = 39 − (32) = 7, so x = 7/1 = 7.
37
If -3x − 2y = 7 and -6x + y = 94, what is x + y?
Medium
ExplanationSolving the system gives x = -13 and y = 16, so x + y = 3.
38
A delivery service charges a fixed fee of Rs. 11 plus Rs. 22 per item. If a customer has a budget of Rs. 372, what is the maximum number of items they can order?
Medium
Explanation11 + 22n ≤ 372, so n ≤ 361/22 ≈ 16.41, meaning at most 16 items.
39
Solve for x: -4x − 18 > -10
Medium
ExplanationDividing both sides by the negative coefficient -4 reverses the inequality sign, giving x < -2.
40
Solve for x: -65 < 7x + 5 < 26
Medium
ExplanationSubtracting 5 from all parts: -70 < 7x < 21. Dividing by 7: -10 < x < 3.
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41
What is the value of -3x + 23 when x = -16?
Medium
Explanation-3(-16) + 23 = 48 + 23 = 71.
42
Solve for x: x/11 + x/8 = -95
Medium
ExplanationCombining terms: x(1/11 + 1/8) = -95, so x × (19)/88 = -95, giving x = -440.
43
Solve for x: -11x + 15 > 202
Medium
ExplanationDividing both sides by the negative coefficient -11 reverses the inequality sign, giving x < -17.
44
Solve the system for y: 5x + 6y = 37, -9x + 6y = 51
Medium
ExplanationSolving the system by elimination or substitution gives y = 7 (and x = -1).
45
Solve for x: -7x + 22 > -76
Medium
ExplanationDividing both sides by the negative coefficient -7 reverses the inequality sign, giving x < 14.
46
Solve for x: x/9 − 24 = -12
Medium
Explanationx/9 = -12 − (-24) = 12, so x = 9 × 12 = 108.
47
Solve for x: x/5 − 9 = -18
Medium
Explanationx/5 = -18 − (-9) = -9, so x = 5 × -9 = -45.
48
Solve the system for x: -7x + 8y = -98, 4x + 5y = -78
Medium
ExplanationSolving the system by elimination or substitution gives x = -2 (and y = -14).
49
Solve for x: -10x − 26 > 104
Medium
ExplanationDividing both sides by the negative coefficient -10 reverses the inequality sign, giving x < -13.
50
If x − 6y = 32 and -x − 6y = 28, what is x + y?
Medium
ExplanationSolving the system gives x = 2 and y = -5, so x + y = -3.
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51
Solve for x: -6(x + 7) = -18
Medium
ExplanationDividing both sides by -6: x + 7 = 3, so x = -4.
52
If 3x + 9y = -15 and 7x − 9y = -35, what is x + y?
Medium
ExplanationSolving the system gives x = -5 and y = 0, so x + y = -5.
53
Given 2x + 3y = -24, what is y when x = 24?
Medium
Explanation3y = -24 − 2(24) = -24 − 48 = -72, so y = -72/3 = -24.
54
A cinema sells adult tickets for Rs. 25 and child tickets for Rs. 21. If 39 tickets were sold for a total of Rs. 859, how many adult tickets were sold?
Medium
ExplanationLet a = adult tickets, c = child tickets. a + c = 39 and 25a + 21c = 859. Solving gives a = 10, c = 29.
55
A delivery service charges a fixed fee of Rs. 16 plus Rs. 3 per item. If a customer has a budget of Rs. 104, what is the maximum number of items they can order?
Medium
Explanation16 + 3n ≤ 104, so n ≤ 88/3 ≈ 29.33, meaning at most 29 items.
56
What is the slope of the line through (-4, 11) and (-7, -6)?
How many solutions does the equation 10x + 18 = 10x + 18 have?
Medium
ExplanationBoth sides are identical for every x, so every value of x works — infinitely many solutions.
74
Solve for x: -14x − 8 > 216
Medium
ExplanationDividing both sides by the negative coefficient -14 reverses the inequality sign, giving x < -16.
75
A delivery service charges a fixed fee of Rs. 33 plus Rs. 30 per item. If a customer has a budget of Rs. 549, what is the maximum number of items they can order?
Medium
Explanation33 + 30n ≤ 549, so n ≤ 516/30 ≈ 17.20, meaning at most 17 items.
76
Solve for x: -2x − 29 < -53
Medium
ExplanationDividing both sides by the negative coefficient -2 reverses the inequality sign, giving x > 12.
77
What is the slope of the line through (-16, 9) and (-25, 14)?
A delivery service charges a fixed fee of Rs. 28 plus Rs. 28 per item. If a customer has a budget of Rs. 238, what is the maximum number of items they can order?
Medium
Explanation28 + 28n ≤ 238, so n ≤ 210/28 ≈ 7.50, meaning at most 7 items.
79
Solve for x: x/-6 + 20 = 14
Medium
Explanationx/-6 = 14 − (20) = -6, so x = -6 × -6 = 36.
80
Solve for x: x/12 + 9 = -6
Medium
Explanationx/12 = -6 − (9) = -15, so x = 12 × -15 = -180.
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81
Solve for x: x/-6 − 18 = -27
Medium
Explanationx/-6 = -27 − (-18) = -9, so x = -6 × -9 = 54.
82
What is the slope of the line through (10, -15) and (8, -23)?
If 7x + 4y = -48 and -8x − 7y = 101, what is x + y?
Medium
ExplanationSolving the system gives x = 4 and y = -19, so x + y = -15.
86
Solve for x: x/3 + x/4 = 56
Medium
ExplanationCombining terms: x(1/3 + 1/4) = 56, so x × (7)/12 = 56, giving x = 96.
87
A delivery service charges a fixed fee of Rs. 29 plus Rs. 25 per item. If a customer has a budget of Rs. 751, what is the maximum number of items they can order?
Medium
Explanation29 + 25n ≤ 751, so n ≤ 722/25 ≈ 28.88, meaning at most 28 items.
88
If 3x + 2y = 25 and -4x − y = -35, what is x + y?
Medium
ExplanationSolving the system gives x = 9 and y = -1, so x + y = 8.
89
If 8x + 3y = 56 and x − 7y = 7, what is x + y?
Medium
ExplanationSolving the system gives x = 7 and y = 0, so x + y = 7.
90
A cinema sells adult tickets for Rs. 12 and child tickets for Rs. 10. If 84 tickets were sold for a total of Rs. 890, how many adult tickets were sold?
Medium
ExplanationLet a = adult tickets, c = child tickets. a + c = 84 and 12a + 10c = 890. Solving gives a = 25, c = 59.
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91
Solve for x: x + 3 ≤ -11
Medium
Explanationx ≤ -11 − (3) = -14, so x ≤ -14.
92
Solve for x: -5x + 23 > 38
Medium
ExplanationDividing both sides by the negative coefficient -5 reverses the inequality sign, giving x < -3.
93
Solve the system for y: -2x − 7y = -75, 5x − 9y = -210
Medium
ExplanationSolving the system by elimination or substitution gives y = 15 (and x = -15).
94
Solve for x: -10x + 27 = -183
Medium
Explanation-10x = -183 − (27) = -210, so x = -210/-10 = 21.
95
Solve for x: 4x + 14 = 12x − 82
Medium
ExplanationMoving variable terms to one side: (4−12)x = -82−(14), so x = (-96)/(-8) = 12.
96
Solve for x: 9x + 19 > -98
Medium
Explanation9x > -98 − (19) = -117, so x > -13.
97
Solve for x: -1 < x + 17 < 12
Medium
ExplanationSubtracting 17 from all parts: -18 < 1x < -5. Dividing by 1: -18 < x < -5.
98
A delivery service charges a fixed fee of Rs. 5 plus Rs. 23 per item. If a customer has a budget of Rs. 471, what is the maximum number of items they can order?
Medium
Explanation5 + 23n ≤ 471, so n ≤ 466/23 ≈ 20.26, meaning at most 20 items.
99
A jar contains only Rs. 5 and Rs. 10 coins. There are 77 coins with a total value of Rs. 685. How many Rs. 10 coins are there?
Medium
ExplanationLet x = Rs.5 coins, y = Rs.10 coins. x + y = 77 and 5x + 10y = 685. Solving gives x = 17, y = 60.
100
Solve the system for y: 2x + 5y = 42, 5x + 2y = -21
Medium
ExplanationSolving the system by elimination or substitution gives y = 12 (and x = -9).