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? (Points : 2)
S = 4B
3.6S + 4.25B = 3730
Substitute 4B for S in second equation and solve for B. Insert that value into the first equation and solve for S. Check by inserting both values into the second equation.
To solve this problem, let's set up equations based on the given information:
Let's represent the number of banana splits sold as "b" and the number of sundaes sold as "s".
We know that the cost of one banana split is $4.25 and the cost of one sundae is $3.60. Therefore, the total sales from banana splits can be calculated as 4.25b, and the total sales from sundaes can be calculated as 3.60s.
From the problem statement, we also know that the shop sold four times as many sundaes as banana splits, so we can write the equation:
s = 4b
The total sales from banana splits and sundaes combined is given as $3,730, so we can write the equation:
4.25b + 3.60s = 3,730
Now we have a system of two equations:
s = 4b (Equation 1)
4.25b + 3.60s = 3,730 (Equation 2)
To solve this system of equations, we can substitute Equation 1 into Equation 2 to eliminate the variable "s":
4.25b + 3.60(4b) = 3,730
4.25b + 14.40b = 3,730
18.65b = 3,730
b = 3,730 / 18.65
b ≈ 200
Therefore, approximately 200 banana splits were sold.