using equations

Question

Dave has 2 buckets that he uses to fill the water troughs on his horse farm. He wants to determine how many ounces each bucket holds. On Tuesday, he fills an empty 2000 ounce water trough with 7 large buckets and 5 small buckets of water. On Thursday, he fills the same empty water trough with 4 large buckets and 10 small buckets of water. How many ounces does each bucket hold? 

Answer 1

What are the quantities involved?

let L be size (ounces) of Large bucket

let S be size of small bucket

what equations relate these quantities? The first one is Tuesdays filling, the second is Thursday’s filling.

2000 = 7L + 5S

2000 = 4L + 10S

Since your unit is “using equations” I assume you know how to solve now that you’ve got two equations. 

 

Heres a hint, multiply the first equation by 2 and subtract the second line. This gives just one equation, involving L. Solve for L, then substitute that value  in either equation, and solve for S.