Philip P. answered • 03/25/14

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Let x = the unknown cost of a single hot dog and y = the unknown cost of a single soft drink. We have two unknowns so we need two equations to find them.

Equation 1 -

*10 hot dogs and 5 soft drinks cost $35*; that is 10x + 5y = 35Equation 2 -

*7 hot dogs and 4 soft drinks cost $25.25*; that is 7x + 4y = 25.25First let's re-write equation 1 to solve for y:

10x + 5y = 35

5y = 35 - 10x (subtract 10x from both sides)

y = 7 - 2x (divide both sides by 5)

Next, let's substitute 7 - 2x for y in equation 2:

7x + 4y = 25.25

7x + 4(7-2x) = 25.25

7x + 28 - 8x = 25.25

-x + 28 = 25.25

x - 28 = -25.25

Solve for x, the cost of a single hot dog. Once you have that, use y = 7 - 2x to find the cost of a single soft drink.