Equations in Word Problems Help
Equations in Word Problems
Equations can be used to solve word problems in algebra.
After reading the problem:
- Step 1 Represent one of the unknown quantities as x and the other unknown by an algebraic expression in terms of x.
- Step 2 Write an equation using the unknown quantities.
- Step 3 Solve the equation for x and then find the other unknown.
- Step 4 Check the answers.
One number is 8 more than another number. The sum of the two numbers is 114. Find the numbers.
Hence, one number is 53 and the other number is 61.
Step 4 Check: 53 + 61 = 114.
A carpenter cuts a board 72 inches long into two pieces. One piece is twice as long as the other. Find the lengths of the pieces.
Hence, one piece is 24 inches long and the other piece is 48 inches long.
Step 4 Check: 24 inches + 48 inches = 72 inches
$40 in tips is to be divided among three food servers. The first server gets twice as much as the second server since he worked twice as long; the third server gets $7. Find the amount each server received.
Hence, the first server received $22, the second server received $11, and the third server received $7.
Step 4 Check: $22 + $11 + $7 = $40
Equations in Word Problems Practice Problems
1. A stick 56 inches long is broken into two pieces so that one piece is 28 inches longer than the other piece. Find the length of each piece.
2. A person made two purchases. One purchase costs four times as much as the other purchase. The total cost of both purchases was $28. Find the cost of each purchase.
3. The difference between two numbers is 12. Find the values of each of the numbers if their sum is 28.
4. A mother is 4 times older than her daughter. In 14 years, she will be twice as old as her daughter. Find their ages now.
5. A house is worth four times as much as the lot it is built on. If the sum of the values of the house and lot is $156,000, find the value of each.
1. 14 inches, 42 inches
2. $5.60, $22.40
3. 8, 20
4. mother's age = 28; daughter's age = 7
5. lot's value = $31,200; house's value = $124,800
Practice problems for this concept can be found at: Expressions And Equations Practice Test.
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