Algebra: how many​ 5-cent bottles or cans, and how many​ 10-cent bottles or cans were​ collected?

Question

As part of a​ fundraiser, a local organization collected 424 returnable bottles and​ cans, some worth 5 cents each and the rest worth 10 cents each. If the total value of the cans and bottles was ​$25.45​, how many​ 5-cent bottles or cans, and how many​ 10-cent bottles or cans were​ collected?

Answer 1

424 = F + T

5F + 10T = 2545

5F + 5T = 2120 multiply the 1st equation by 5 and subtract from 2nd equation to get

5T = 425 divide both sides by 5

T = 425/5 = 85 of the 10 cent bottles

F = 424-85 = 339 of the 5 cent bottles

5(339) + 10(85) = 1695 + 850 = 2545