Question

rachel played a few games of bowling. the first game she scored one hundred two less than the third game. the second game she scored twenty - four more than the first game. her total score for the first two games was 238. if she wants an average score of 156, what must she score on the fourth game?

Explanation:

Step1: Define variables for scores

Let the score of the first game be \( x \), the second be \( y \), the third be \( z \), and the fourth be \( w \).

Step2: Use first two game total

We know \( x + y = 238 \). Also, \( y = x + 24 \). Substitute \( y \) into the first equation: \( x+(x + 24)=238 \). Simplify: \( 2x+24 = 238 \). Subtract 24: \( 2x=238 - 24=214 \). Divide by 2: \( x=\frac{214}{2}=107 \). Then \( y = 107 + 24 = 131 \).

Step3: Find third game score

Given \( x=z - 102 \), so \( z=x + 102=107+102 = 209 \).

Step4: Use average for four games

Average score of 4 games is 156, so total score for 4 games is \( 156\times4 = 624 \). The sum of first three games is \( x + y+z=107 + 131+209 = 447 \).

Step5: Find fourth game score

Total of four games: \( x + y+z+w=624 \). So \( w=624-(x + y+z)=624 - 447 = 177 \).

Answer:

177