Question

solving linear equations using the distributive property
raj and aditi like to play chess against each other. aditi has won 12 of
the 20 games so far. they decide to play more games.
how many more games will aditi have to win to have a 70% winning
record?
12 + x = 0.70(20 + x)
x = \\(\frac{2}{3}\\) ≈ 6.67
she will have to win 7 more games to have a 70% winning record.
how many more games will aditi have to win to have an 80% winning
record?
the linear equation that models this is
aditi would have to win more games to have an 80% winning
record.

Explanation:

Step1: Define Variables and Equation

Let \( x \) be the number of additional games Aditi wins. Total wins will be \( 12 + x \), total games will be \( 20 + x \). For 80% winning record, the equation is \( 12 + x = 0.80(20 + x) \).

Step2: Solve the Equation

Expand the right side: \( 12 + x = 16 + 0.8x \). Subtract \( 0.8x \) from both sides: \( 12 + 0.2x = 16 \). Subtract 12: \( 0.2x = 4 \). Divide by 0.2: \( x = \frac{4}{0.2} = 20 \).

Answer:

The linear equation is \( 12 + x = 0.80(20 + x) \), and Aditi would have to win 20 more games.