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Consecutive Integers
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100
Find two consecutive integers whose sum is -29.
-15, -14 x + (x+1) = -29
100
The second of two numbers is 4 times the first. Their sum is 50. Find the two numbers.
x + 4x = 50. 10, 40
100
The fastest speed recorded for a cheetah is 70 mph. This is 11 mph less than 3 times the fastest running speed for a man. What is the fastest running speed for a man?
m = man's speed 3m - 11 = 70 27 mph
100
The length of a rectangle is 3 times the width. The perimeter is 96cm. Find the width and length.
w = width 2(w + 3w) = 96 w = 12, l = 36
100
seven times a number is the same as 12 more than 3 times the number. Find the number.
7x = 12 +3x x = 3
200
Find three consecutive integers whose sum is -148.
x + (x+1) + (x+2) = -147. -50, -49, -48
200
The larger of two numbers is 12 more than the smaller. Their sum is 84. Find the numbers.
x + (x+12) = 84 36, 48
200
The Empire State Building is 1250 feet tall. this is 140 feet more than twice the height of the Washington monument.How tall is the Washington monument?
w = washington monument height 2w + 140 = 1250 w = 555 feet
200
The length of a rectangle is 5m greater than the width. The perimeter is 150 m. Find the width and length.
w = width. 2(w+w+5) = 150 w = 35 m, l = 40 m
200
Three less than 11 times a a number is the same as the number decreased by 13. Find the number.
11x - 3 = x - 13 x = -1
300
Find two consecutive even integers whose sum is 66.
x + (x+2) = 66 32, 34
300
The sum of two numbers is 45. The first is 9 less than the second. Find the numbers.
(x - 9) + x = 45 18, 27
300
Steve can bench-press 72 pounds. This is 3/4 of the pounds Ricky can bench-press. How many pounds can Ricky benchpress?
r = pounds ricky can bench-press (3/4)r = 72 r = 96 pounds
300
The width of a rectangle is 12 cm less than the length. The perimeter is 156 cm. Find the width and length.
l = length 2(l + l - 12) = 156 OR w = width 2 (w + w + 12) = 156 w = 33m, l = 45m
300
Six more than 5 times the number is the same as 9 less than twice the number. find the number.
5x + 6 = 2x - 9 x = -5
400
Find four consecutive odd integers whose sum is 56.
x + (x+2) + (x+4) + (x+6) = 56, 11, 13, 15, 17
400
The larger of two numbers is 1 less than three times the smaller. Their sum is 63. Find the numbers.
x + (3x - 1) = 63 16, 47
400
The width of a singles tennis court is 27 feet. This is 1 foot more than 1/3 of the length. What is the length of the court?
x= length of the court (1/3)x + 1 = 27 x = 78 feet
400
The perimeter of a triangle is 76 cm. Side 'a' is twice as long as side 'b', and side 'c' is 1cm longer than side a. Find the length of each side. (Equation must be written with only 1 variable).
If a = length of side a a + (a/2) + (a+1) = 76 a = 30 cm If b = length of side b, 2b + b + (2b + 1) = 76 b = 15cm a= 30, b = 15, c = 31
400
Ten increased by 6 times a number is the same as 4 less than 4 times the number. Find the number.
10 + 6x = 4x - 4 x = -7
500
Find two consecutive even integers such that the sum of the larger and twice the smaller is 62.
(x+2) + 2x = 62 20, 22
500
The sum of two numbers is 172. The first is 8 less than 5 times the second. Find the first number.
(5x - 8) + x = 172 142 is the first number.
500
a golf ball can travel 170 mph. This is 1 and 3/7 times the fastest speed recorded for a hockey puck. What is the record speed for a hockey puck? *100 point bonus for the answer in kilometers per hour*
p = puck speed (10/7)p = 170 p = 119 mph (about 200 kph)
500
Th length of a rectangle is 3 times the width. IF the length is decreased by 4m and the width is increased by 1m, the perimeter will be 66 meters. Find the dimensions of the original rectangle.
w = width (length = 3w) 2((3w - 4) + (w + 1)) = 66 w = 9, l = 27
500
eight times a number plus 3 times the number is the same as 9 more than 12 times the number. find the number.
8x + 3x = 9 + 12x x = -9