Solving Multi-Step Equations
Solve each equation.
VI. Word Problems
1. One number is 5 more than twice another number. The sum of the numbers is 35. Find the numbers.
2. Ms. Jones invested $18,000 in two accounts. One account pays 6% simple interest and the other pays
8%. Her total interest for the year was $1,290. How much did she have in each account?
3. How many liters of a 40% solution and an16% solution must be mixed to obtain 20 liters of a 22%
solution?
4. Sheila bought burgers and fries for her children and some friends. The burgers cost $2.05 each and the
fries are $.85 each. She bought a total of 14 items, for a total cost of $19.10. How many of each did
she buy?
Word Problems Answers
1. Let x = “another number” forcing 2x + 5 = “One number.” x + 2x + 5 = 35 and x = 10.
“One number” = 25 and “another number” = 10.
2. Let x = the dollars in the account paying 6% interest
Then, 18,000 – x = the dollars in the account paying 8%.
The interest dollars are calculated by multiplying the total dollars in the account by the interest rate.
Hence: .06 x = the interest earned by the first account
.08 (18,000 – x) = the interest earned by the second account. Adding up all the interest,
.06x + .08(18,000 – x) = 1,290. Solving, x = 7,500. So, Ms. Jones has $7,500 in the account paying
6% interest and $10,500 in the account paying 8% interest.
3. Use the following buckets:
From the diagram, we get the equation: .4x + .16 (20 – x) = 20(.4)
x = 5 and the answer is 5 liters at 40% and 15 liters at 16%.
4. Let x = the number of burgers and 14 – x = the number of fries. To get the total amount of money
spent, multiply the number of items by the cost of the item. 2.05 x = the total dollars spent on burgers
and .85 (14 – x) = the total dollars spent on fries. The equation is: 2.05x + .85 (14 – x) = 19.10.
Solving the equation, x = 6. Hence, she bought 6 burgers and 8 fries.(x) + (20 - x) = (20 liters)
40 % 16 % 40 %
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