WORD PROBLEMS
Find each answer. Write an equation and then solve.
1)
The sum of a number and 8 is the opposite of -8.
2)
Twenty less than five times a number, divided by 2, is fifteen.
3)
Three times the sum of four and a number is twice the number.
4) 55 more than a number is twenty.
5)
One-third of a number is --12.
6) Six times a number increased by 3 is 33.
7)
Two times the sum of nine and a number is the opposite of 9.
8) Ten less than twice a number is 26.
9) The quotient of five and a number decreased by three is --5.
10) If we increase a number by 12 and divide it by 2, the result is 14.
11) Half of a number is equal to 8 more than the number.
12) Three times the difference of eight and twice a number is five times the number.
13) A number divided by three is nine more than the number.
14) The perimeter of a rectangular pool is 130 ft. The width is 4 times the length. Find the
dimensions of the pool.
15) In a triangle, one angle is 40 more than the smallest angle and the third angle is half the sum of
the other two angles. Find the measure of each angle.
16) Find two consecutive odd integers whose sum is 160.
17)
Find three consecutive integers whose sum is 186.
18)
Trisha has a bag with 32 dimes and nickels worth $2.80. How many of each coin does she have?
19) Carlos invested $5400. Some money was invested at 7.5% and the rest at 6% per year. How
much did he invest at each amount if his interest earned was $384?
20) Pasha has a box with 40 coins consisting of dimes, quarters and nickels that are worth $5.25.
There are 5 more nickels than quarters. How many of each coin does she have?
21) Slatko invested some money at 8 3/4% interest per year and half as much money at 9%. How
much money did he invest at each rate if the total annual interest was $3047.50?
22) The length of a rectangle is 5 cm less than 3 times its width. If the perimeter of the rectangle is
54 cm, find the length and width.
23) The width of a garden is 4 cm more than 3 times its length. The perimeter of the garden is 55 cm.
What are the dimensions of the garden?
24)
In a triangle, one angle is twice the smallest angle and the third angle is 40 more than the
smallest angle. Find all three angles.
25) One side of a triangle is 7 inches shorter than the longest side. The third side is 3 inches shorter
than the longest side. The perimeter is 26 inches. Find the lengths of all three sides.
26) Find two consecutive integers whose sum is 139.
27) Find 3 consecutive odd integers whose sum is 171.
28) A newspaper stand has 200 coins at the end of the day, all dimes and quarters. If the value of the
coins is $42.50, how many of each coin were in the stand?
29) A bank teller had 125 bills in $10 and $20 bills to start the day. If the total in her register was
$1650, how many of each bill did the teller start off with?
30) Gary has a box of coins that he uses when playing poker. The box currently contains 53 coins
consisting of nickels, dimes and quarters. The number of quarters is equal to the number of nickels.
The total value of the coins is $6.80. How many of each type of coin does Greg have in the box?
31) In the 19th Century, the U.S. minted two-cent coins and three-cent coins. Chandra has three times
as many three-cent coins as two-cent coins. The face value of the coins is $1.10. How many of each
coin does she have?
Answer Key
If you find an error, please contact Anna Fisher at Anna_Fisher@Bloomfield.edu. Please include the
following information: worksheet title and the problem number.
1) x + 8 = -(-8)
x=0
2) 5x – 20 = 15
2
x = 10
3) 3(4 + x) = 2x x = -12
4) 55 + x = 20 x = -35
5) 1/3x = -12 x = -36
6) 6x + 3 = 33 x = 5
7) 2(9 + x) = -9 x = -27/2
8) 2x – 10 = 26 x = 9
9) 5 – 3 = -5
x
10) n + 12 = 14 x = 16
2
11) 1/2x = 8 + x x = -16
x = -5/2
12) 3(8 – 2x) = 5xx = 24/11
13) x/3 = 9 + x x = -27/2
14) Let length be x; 2(4x) + 2(x) = 130; length = 13 ft, width = 52 ft
15) Let x be the smallest angle; (40 + x) + x + ½(x + 40 + x) = 180; angle measures are 40, 60, 80
16) Let x be the first number; x + x + 2 = 160;
the two numbers are 79 and 81
17) Let x be the first number; x + x + 1 + x + 2 = 186; the three numbers are 61, 62, 63
18) Let x be dimes; .10(x) + .05(32 – x) = 2.80;
dimes = 24 and nickels = 8
19) Let x be the amount for 7.5%; .075(x) + .06(5400 – x) = 384; $4000 at 7.5% and $1400 at 6%
20) Let x be quarters; .05(5 + x) + .25(x) + .10(35 – 2x) = 5.25; quarters = 15, dimes = 5, nickels = 20
21) Let x be the amount for 8 ¾ %; .0875(x) + .09(1/2 x) = 3047.50; $23,000 at 8 ¾ % and
$11,500 at 9%
22) Let x be the width; 2(x) + 2(3x – 5) = 54; width = 8 cm and length = 19 cm
23) Let x be the length; 2(x) + 2(4 + 3x) = 55; length = 5 7/8 cm and width = 21 5/8 cm
24) Let x be smallest angle; x + 2x + 40 + x = 180; angle measures are 35, 70, 75
25) Let x be longest side; x + (x – 7) + (x – 3) = 26; lengths of sides are 9 in, 6 in, 2 in
26) Let x be the first number; x + (x + 1) = 139; the two numbers are 69, 70
27) Let x be the first number; x + (x + 2) + (x + 4) = 171; the three numbers are 55, 57, 59
28) Let x be quarters; .25(x) + .10(200 – x) = 42.50; quarters = 150 and dimes = 50
29) Let x be the $10 bill; 10(x) + 20(125 – x) = 1650; $10 bills = 85 and $20 bills = 40
30) Let x be the nickels; .05(x) + .25(x) + .10(53 – 2x) = 6.80; nickels = 15, quarters = 15, dimes =
23
31) Let x be the 2-cent coin; .02(x) + .03(3x) = 1.10; 2-cent coin = 10 and 3-cent coin = 30