How do you find the cost of a gallon of water if the cost of a gallon of milk is $0.50 more than five times the cost of a gallon of water and if a gallon of milk costs $3.75?

Problems like this can be confusing because it's hard to figure out how to express amounts like "$0.50 more than five times the cost of a gallon of water."

The trick is to write the math expression one step at a time.

Find a way to express the cost of a gallon of milk

Let `x` represent the cost of a gallon of water

Cost of water . . . . . . . . . `x` `larr` cost of a gallon of water
`5` times as much . . . . . .`5x`
`50ȼ` more than that . . . `5x + 50` `larr` cost of a gallon of milk

Write the equation and solve for `x`

`5x + $0.50 = $3.75`
Solve for `x`, already defined as "the cost of a gallon of water"

1) Subtract `$0.50` from both sides to isolate the `5x` term
`5x = $3.25`

2) Divide both sides by `5` to isolate `x`, already defined as "the cost of a gallon of water"
`x = $0.65` `larr` answer for "the cost of a gallon of water"

Answer
A gallon of water costs `$0.65`

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Check

`1` gallon of water . . . . . `$0.65`
`5` times that . . . . . . . . . .`$3.25`
50ȼ more than that . .. .`$3.75`   ✓

`Check`