# 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?

Mar 4, 2018

A gallon of water costs $0.65 #### Explanation: 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 . . . . . . . . . $x$ $\leftarrow$ cost of a gallon of water
$5$ times as much . . . . . .$5 x$
50ȼ more than that . . . $5 x + 50$ $\leftarrow$ 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 $5 x$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 $\leftarrow$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 ✓ $C h e c k\$