Question

The 10th-grade class officers ordered t-shirts and sweatshirts to sell as a fundraiser. Each t-shirt weighed StartFraction one-half EndFraction. of a pound, and each sweatshirt weighed StartFraction 3 Over 4 EndFraction of a pound. The total weight of the contents of the box was 43 and StartFraction 3 Over 4 EndFraction pounds. Which equation written in standard form represents the number of t-shirts, t, and the number of sweatshirts, s, that were ordered?

StartFraction one-half EndFraction t plus StartFraction 3 Over 4 EndFraction s equals 43 and StartFraction 3 Over 4 EndFraction
StartFraction 3 Over 4 EndFraction s equals negative StartFraction one-half EndFraction s plus 43 and StartFraction 3 Over 4 EndFraction.
2t + 3s = 175
3s = –2t + 175

Answer 1

Each t-shirt weighs 1/2 lb and each sweatshirt 3/4 lb, so (1/2)t + (3/4)s = 43 3/4. Multiply both sides by 4 to clear fractions: 2t + 3s = 175. Thus the standard-form equation is 2t + 3s = 175.