back to Algebra 1 video lessons

How to translate word sentence into algebra expression and write one variable equation?

Question:

A store shipped 510 pounds of apples and oranges. After selling one-thirds of apples and one-quarter of oranges, the remaining weights of the two fruits is equal. How many pounds of the original apples and oranges?

Solution:

Let the original apples be x pounds
so, the original oranges are 510 - x pounds
sold apples are (1/3) x pounds
Sold oranges are (1/4) (510 - x) pounds
leftover apples are (2/3) x pounds
leftover oranges are (3/4) (510 - x) pounds
relationship: the remaining weights of the two fruits is equal
(2/3) x = (3/4) (510 - x)
remove denominator by multiply 12 in both side of the equation
(12) (2/3) x = (12) (3/4) (510 - x)
(4) 2x = (3) (3) (510 - x)
8x = 9 (510 - x)
8x = 9 × 510 - 9x
8x + 9x = 9 × 510
17x = 9 × 510
x = 9 × 510/17 = 270
510 - x = 510 - 270 = 240

The original apples are 270 pounds and original oranges are 240 pounds.