Question 1037464
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.