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At a community barbecue, Mrs. Whitehead and Mr. Howell are buying dinner for their families. Mrs. Whitehead purchases 2 hot dog meals and 3 hamburger meals, paying a total of $35. Mr. Howell buys 1 hot dog meal and 3 hamburger meals, spending $31 in all. How much do the meals cost? Hot dog meals cost $ each, and hamburger meals cost $ each.

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ANSWERS

Hot dog meal: $4

Hamburger meal: $9

EXPLANATION

We can write a system of equations

• x: cost of each hot dog meal

,

• y: cost of each hamburger meal

Mrs. Whitehead bought 2 hot dog meals and 3 hamburger meals and spent $35:

[tex]2x+3y=35[/tex]

Mr. Howell bought 1 hot dog meal and 4 hamburger meals and spent $31:

[tex]x+3y=31[/tex]

The system of equations is:

[tex]\begin{cases}2x+3y=35 \\ x+3y=31\end{cases}[/tex]

Using the elimination method - which consists in subtracting one equation from the other in order to eliminate one of the variables - we can find

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