Question

cooper buys ice cream and onions at the store.

• he pays a total of $39.55.
• he pays $3.15 for the ice cream.
• he buys 8 bags of onions that each cost the same amount.

which tape diagram could be used to represent the context if b represents how much each bag of onions costs?

Explanation:

Since the problem is about finding the cost of each bag of onions and representing it with a tape diagram, we can first establish the equation. The total cost is the cost of ice cream plus the cost of 8 bags of onions. Let \( b \) be the cost of each bag of onions. Then the total cost equation is: \( 3.15 + 8b = 39.55 \).

A tape diagram for this situation would have one part labeled \( \$3.15 \) (for the ice cream) and another part with 8 equal sections each labeled \( b \) (for the 8 bags of onions), and the total length of the tape diagram would represent \( \$39.55 \).

To find the value of \( b \) (though the question is about the tape diagram, we can also solve for \( b \) to understand the context better):

Step 1: Subtract the cost of ice cream from the total cost

We know the total cost is \( \$39.55 \) and the ice cream costs \( \$3.15 \). So we subtract \( 3.15 \) from \( 39.55 \) to find the total cost of the 8 bags of onions.
\( 39.55 - 3.15 = 36.4 \)

Step 2: Divide the total cost of onions by the number of bags

There are 8 bags of onions, and their total cost is \( \$36.4 \). So we divide \( 36.4 \) by \( 8 \) to find the cost per bag (\( b \)).
\( b = \frac{36.4}{8} = 4.55 \)

But the main question is about the tape diagram. The correct tape diagram should have a segment for \( \$3.15 \) and 8 equal segments each labeled \( b \), with the sum of all segments equal to \( \$39.55 \).

Answer:

The tape diagram should have one part labeled \(\$3.15\) (for ice cream) and another part with 8 equal parts each labeled \(b\) (for onions), such that \(\$3.15 + 8b=\$39.55\). If we solve for \(b\), each bag of onions costs \(\$4.55\).