McGraw Hill Integrated II, 2012
MH
McGraw Hill Integrated II, 2012 View details
1. Angles of Triangles
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Exercise 55 Page 343

Introduce variables.

E

Practice makes perfect

To be able to use algebra, let's introduce variables and use these variables to write equations to express the information given in the question.

Information Expression
Number of video games Joey has. j
Number of video games Solana has. s
Number of video games Melissa has. m
Joey has 4 more video games than Solana. j=s+4
Joey has half as many video games as Melissa. j=m/2
Together they have 24 video games. j+s+m=24

Notice that we have two equations expressing j in terms of the other variables. We can rearrange these to express s and m in terms of j.

Original Equation Operation Rearranged Equation
j=s+4 Subtract 4 s=j-4
j=m/2 Multiply by 2 m=2j
We can use these expressions to substitute in the last equation.
j+s+m=24
j+ j-4+ 2j=24
â–Ľ
Solve for j
4j-4=24
4j=28
j=7
We already know that m=2j, so m=2(7)=14. Hence, Melissa has 14 video games. The correct answer choice is E.