System of Equations
Let
x = Number of sundaes sold
y = Number of banana splits sold
Sundaes are sold for $2 each and banana splits are sold for $3 each.
If we sell x sundaes, then we make $2x for selling sundaes.
If we sell y banana splits, then we make $3y for selling banana splits
The first condition states they made a total of $150, thus the first equation is:
2x + 3y = 150 [1]
It's also given the number of sundaes sold (x) is 5 more than the number of banana splits sold (y), thus the second equation is:
x = y + 5 [2]
Substituting [2] into [1]:
2(y + 5) + 3y = 150
Operating:
2y + 10 + 3y = 150
Simplifying:
5y + 10 = 150
Subtracting 10:
5y = 140
Dividing by 5:
y = 140/5
y = 28
Substituting in [2]
x = 28+ 5
x = 33
Answer: 33 sundaes and 28 banana splits were sold