Question

1. fill in the blanks using the available answer choices.

martas bowling scores for the first 4 games in a tournament are shown in the table. how many points must she score in the 5th game to earn at least a 140 point average in all 5 games?

game	score
2	125
3	140
4	135

(blank 1) ____ (blank 2) ____ points
blank 1 options

• at least
• at most

blank 2 options

• 165
• 155
• 145
• 135

Explanation:

Step1: Recall average formula

The average of \( n \) numbers is \( \frac{\text{Sum of numbers}}{n} \). For 5 games, average \( \geq 140 \), so total score for 5 games \( \geq 140\times5 = 700 \).

Step2: Calculate sum of first 4 games

Sum of scores: \( 145 + 125 + 140 + 135 \).
\( 145 + 125 = 270 \), \( 140 + 135 = 275 \), total \( 270 + 275 = 545 \).

Step3: Let \( x \) be 5th game score

We need \( 545 + x \geq 700 \). Solve for \( x \): \( x \geq 700 - 545 = 155 \)? Wait, no, 700 - 545 is 155? Wait, 545 + 155 = 700. Wait, but 1405=700. Wait, 145+125=270, 140+135=275, 270+275=545. 700-545=155? Wait, no, 545 + 155 = 700. But wait, the options for Blank 2: 165, 155, 145, 135. Wait, maybe I miscalculated. Wait, 145+125=270, 140+135=275, 270+275=545. 1405=700. So 700-545=155? Wait, but let's check again. Wait, 145+125=270, 140+135=275, 270+275=545. 545 + x ≥ 700 → x ≥ 155. But wait, the options have 155? Wait, no, 700 - 545 is 155? Wait, 545 + 155 = 700. So average would be 700/5=140. So to have at least 140 average, x must be at least 155? Wait, but the Blank 2 options: 165, 155, 145, 135. Wait, maybe I made a mistake. Wait, 145+125=270, 140+135=275, sum is 545. 5 games, average ≥140 → total ≥700. So x ≥700-545=155. So Blank 1: At least, Blank 2: 155? Wait, but let's check the options. Wait, maybe I miscalculated the sum. Wait, 145+125=270, 140+135=275, 270+275=545. 700-545=155. So yes, x ≥155. Wait, but the Blank 2 options include 155. So Blank 1: At least, Blank 2: 155? Wait, no, wait 140*5=700. 545 + x ≥700 → x ≥155. So the 5th game must score at least 155 points. Wait, but the Blank 2 options: 165, 155, 145, 135. So 155 is an option. So Blank 1: At least, Blank 2: 155. Wait, but let's check again. Wait, 145+125=270, 140+135=275, sum 545. 545 + 155 = 700, average 140. So to have at least 140, x must be at least 155. So that's correct.

Answer:

Blank 1: At least, Blank 2: 155
So the answers are:
Blank 1: At least
Blank 2: 155