Question

at david’s store, the cost of six boxes of cereal is $23.26. at savannah’s store, the cost of five boxes of the same cereal is $18.98. compare prices by finding a pair of common values (same number of cereal boxes or same price). round your answers to the nearest cent if necessary.

answer attempt 1 out of 2

at david’s store, \boxed{} boxes of cereal cost $\boxed{}. at savannah’s store, \boxed{} boxes of cereal cost $\boxed{}. \boxed{} store has the better price.

Explanation:

Step1: Find unit price at David's store

To find the unit price (price per box) at David's store, we divide the total cost by the number of boxes. The total cost is $23.26 for 6 boxes. So the unit price \( p_D \) is \( \frac{23.26}{6} \).
\( p_D=\frac{23.26}{6}\approx 3.88 \) (rounded to the nearest cent)

Step2: Find unit price at Savannah's store

To find the unit price at Savannah's store, we divide the total cost by the number of boxes. The total cost is $18.98 for 5 boxes. So the unit price \( p_S \) is \( \frac{18.98}{5} \).
\( p_S=\frac{18.98}{5} = 3.796\approx 3.80 \) (rounded to the nearest cent)

Step3: Compare the unit prices

We can also find the cost for a common number of boxes, say 30 boxes (LCM of 6 and 5).

For David's store: Cost for 30 boxes = \( 30\times p_D = 30\times\frac{23.26}{6}=5\times23.26 = 116.30 \)

For Savannah's store: Cost for 30 boxes = \( 30\times p_S=30\times\frac{18.98}{5} = 6\times18.98=113.88 \)

Now we can see that for 30 boxes, David's store costs $116.30 and Savannah's store costs $113.88. Also, the unit price at David's is ~$3.88 per box and at Savannah's is ~$3.80 per box.

Answer:

At David’s store, 30 boxes of cereal cost $116.30. At Savannah’s store, 30 boxes of cereal cost $113.88. Savannah’s store has the better price.

(Alternatively, using unit prices: At David’s store, 1 box of cereal cost $3.88. At Savannah’s store, 1 box of cereal cost $3.80. Savannah’s store has the better price.)