A Cold Stone Creamery ice cream shop sells sundaes for $3.60 and banana splits for $4.25. The shop sells four times as many sundaes as banana splits. If total sales amounted to $3,730 last weekend, how many banana splits were sold?
s = sundaes
b = banana splits
s = 4b shop sels 4 times as many sundaes as banana splits
3.60(s) +4.25(b) = 3730
replace s with 4b
3.60(4b) + 4.25(b) =3730
Solve for b and then find s from 4 times b.
To solve this problem, we can set up a system of equations.
Let's denote the number of sundaes sold as "x" and the number of banana splits sold as "y".
Given that the price of a sundae is $3.60 and the price of a banana split is $4.25, we can set up the following equations:
1) x = 4y (The shop sells four times as many sundaes as banana splits)
2) 3.60x + 4.25y = 3,730 (The total sales amount to $3,730)
Now we need to solve this system of equations to find the values of x and y.
We can substitute the value of x from equation 1 into equation 2:
3.60(4y) + 4.25y = 3,730
14.4y + 4.25y = 3,730
18.65y = 3,730
Divide both sides of the equation by 18.65:
y = 3,730 / 18.65
y ≈ 199.89
Since you cannot sell a fraction of a banana split, the nearest whole number of banana splits sold is 200. Therefore, 200 banana splits were sold.