We are going to make simultaneous equations.
x will be our $3 ice cream and y will be our $5 ice cream
Equation1 ---- x + y = 50 (the sum of all the ice creams they sell)
Equation 2 ---- 3x + 5y = 180 Sum of all the $3 and $5 ice creams is $180
Since we can't solve for both variables we will put one of the variables in terms of the other.
Take x+y=50 and subtract y from both sides. (I could have done subtracted x - it did not matter). Now we have x= ₋ y +50 (negative y +50)
Now I am going to take equation 2 and replace the x with -y +50
3 (-y +50) + 5y = 180
Now I will use the distributive law on the 3 and what's in the parentheses:
-3y + 150 + 5y = 180
Now I will combine like terms (the -3y and the 5y)
2y + 150 = 180
Now subtract 150 from both sides of the equation
2y = 30
Divide both sides by 2
and get y= 15 They sold 15 ice creams that cost $5 each
Since equation 1 is x+y=50 we can replace y with 15
x + 15 = 50 Now subtract 15 from both sides x = 35
Since x represents the $3 ice creams, they sold 35 of those.
Check:
35 X 3 = $105
15 x 5 = + 75
$180
