Question

the number of calories in a piece of cake is 20 less than three times the number in a scoop of ice cream. the cake and the ice cream together have 620 calories. how many calories are in each

Answer 1

To solve this we must set up a system of equations where x is the number of calories in a peice of cake, and y is the number of calories in a scoop of ice cream. when we do this, we get $x=3y-20$ and $x+y=620$. So, to solve this sytem, you can use many methods, but I will use substitution. if we substitute the first equation for x in the second, we get $3y-20+y=620$. solving for y, we get $y=160$. then substituting this in to the first equation, we get $x=460$. So the answer is there are 460 calories in a peice of cake and 160 calories in a scoop of ice cream.