you ordered a 7:4 of black to red backpacks to give away at a fundraiser. if you ordered 64 of red backpacks, how many black backpacks did you order?

Answer 1

To find the number of black backpacks ordered, we can set up a proportion based on the given ratio of black to red backpacks, which is 7:4.

We know that:

• The ratio of black to red backpacks is 7:4.
• You ordered 64 red backpacks.

Let \( b \) represent the number of black backpacks. According to the ratio, we can express this relationship as:

\[ \frac{b}{64} = \frac{7}{4} \]

To solve for \( b \), we can cross-multiply:

\[ b \cdot 4 = 7 \cdot 64 \]

Calculating \( 7 \cdot 64 \):

\[ 7 \cdot 64 = 448 \]

Now substitute that back into the equation:

\[ 4b = 448 \]

Next, divide both sides by 4:

\[ b = \frac{448}{4} = 112 \]

So, you ordered 112 black backpacks.