Question

rates
calculating rates

1. audra can buy a box of 6 cupcakes for $3.99 or a box of 12 cupcakes for $5.50.

a) calculate the rate for each box of cupcakes. how much does it cost for a single cupcake?
b) which box of cupcakes would be a better deal?

Explanation:

Part (a)

Step 1: Calculate rate for 6 - cupcake box

To find the cost per cupcake for the 6 - cupcake box, we divide the total cost by the number of cupcakes. The total cost of the 6 - cupcake box is $\$3.99$ and the number of cupcakes is 6. So the rate $r_1$ is given by $r_1=\frac{3.99}{6}$.
Calculating this, $r_1 = 3.99\div6 = 0.665$ dollars per cupcake.

Step 2: Calculate rate for 12 - cupcake box

For the 12 - cupcake box, the total cost is $\$5.50$ and the number of cupcakes is 12. The rate $r_2$ is $r_2=\frac{5.50}{12}$.
Calculating this, $r_2=5.50\div12\approx0.458$ dollars per cupcake.

To determine which box is a better deal, we compare the cost per cupcake (the rates) calculated in part (a). A better deal means a lower cost per cupcake. We found that the rate for the 6 - cupcake box is $\$0.665$ per cupcake and for the 12 - cupcake box is approximately $\$0.458$ per cupcake. Since $0.458<0.665$, the 12 - cupcake box has a lower cost per cupcake.

Answer:

The cost per cupcake for the 6 - cupcake box is $\$0.665$ and for the 12 - cupcake box is approximately $\$0.458$.

Part (b)