While shooting at the target, Marco hit nine several times and an eight several times. He hit nine twice as many times as seven and the number of fives hit is for 3 smaller than the number of eights hit. He scored 200 points. What is the total number of hits in the target if he never missed and didn't hit any other number?
(A hit in the nine brings 9 points, in the eight brings 8 points, etc.)
Answers
Given : While shooting at the target, Marco hit nine several times and an eight several times. He hit nine twice as many times as seven and the number of fives hit is for 3 smaller than the number of eights hit. He scored 200 points.
To Find : What is the total number of hits in the target if he never missed and didn't hit any other number?
Solution:
Seven hits = x time
Nine hits = 2x time
5 hits y times
8 hits y + 3 times
Total Hits = x + 2x + y + y + 3
= 3x + 2y + 3
7x + 9(2x) + 5y + 8(y + 3) = 200
=> 25x + 13y = 176
y = 2 => x = 6 is the only integral solution
Hence Total Hits
= 3x + 2y + 3
= 3(6) + 2(2) + 3
= 18 + 4 + 3
= 25
total number of hits in the target = 25
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