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Question 1037464: Mario, luigi, Yoshi, and peach completed in the Nintendo world championship. Mario earned one hundred eighty three points less than five times luigi's scored. Yoshi earned one hundred seventy seven points more than three times luigi's score. Peach earned one hundred seventy nine points less than four times luigi's score. The average score of the four players was two hundred, eighty two points. Find the score of each competitor. What place did each competitor come in ?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! let l = luigi's score.
leg m = mario's score.
let y = yoshi's score.
let p = peach's score.
mario earned 183 less than 5 times luigi's score.
yoshi earned 177 more than 3 times luigi's score.
peach earned 179 less than 4 times luigi's score.
the average of all the scores was 182.
your formulas are as follows:
(m+y+p+l)/4 = 282
multiply both sides of this equation by 4 to get:
(m+y+p+l) = 1128
m = 5*l - 183
y = 3*l + 177
p = 4*l - 179
l = l
replace m, y, and p with their equivalents and the formula of (m+y+p+l) = 1128 becomes:
5*l - 183 + 3*l + 177 + 4*l - 179 + l = 1128
combine like terms to get:
13*l - 185 = 1128
add 185 to both sides of this equation to get 13*l = 1128 + 185.
simplify to get 13*l = 1313.
divide both sides of this equation by 13 to get l = 101.
when l = 101 .....
m = 5*l - 183 becomes 5*101 - 183 which is equal to 322.
y = 3*l + 177 becomes 3*101 + 177 which is equal to 480.
p = 4*l - 179 becomes 4*101 - 179 which is equal to 225.
l = l becomes l = 101 which is equal to 101.
add them all together and you get m+y+p+l = 322+480+225+101 = 1128.
divide 1128 by 4 and you get an average of 282.
solution looks good.
solution is:
yoshi came in first with 480.
mario came in second with 322.
peach came in third with 225.
luigi came in last with 101.
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