Use the table to answer the question. White Blue 3 4 x 8 9 12 12 y For every 4 blue crayons in a box, there are 3 white ones. How many white crayons are there if there are 8 blue ones? How many blue crayons are there if there are 12 white ones? Responses 12; 16 12; 16 - no response given 4; 8 4; 8 - no response given 6; 16 6; 16 - no response given 9; 12

Answer 1

Based on the information given in the problem, we can set up a ratio of white crayons to blue crayons. The ratio of white to blue crayons is given as 3:4.

1. If there are 8 blue crayons:

   • Using the ratio, we can set up the following proportion: \[ \frac{\text{White}}{\text{Blue}} = \frac{3}{4} \] If there are 8 blue crayons, we can find the number of white crayons: \[ \frac{3}{4} = \frac{\text{White}}{8} \] Cross-multiplying gives: \[ 3 \cdot 8 = 4 \cdot \text{White} \] \[ 24 = 4 \cdot \text{White} \] \[ \text{White} = \frac{24}{4} = 6 \]

2. If there are 12 white crayons:

   • Again using the same ratio: \[ \frac{\text{White}}{\text{Blue}} = \frac{3}{4} \] If there are 12 white crayons, we can find the number of blue crayons: \[ \frac{3}{4} = \frac{12}{\text{Blue}} \] Cross-multiplying gives: \[ 3 \cdot \text{Blue} = 4 \cdot 12 \] \[ 3 \cdot \text{Blue} = 48 \] \[ \text{Blue} = \frac{48}{3} = 16 \]

From the calculations, we find:

• When there are 8 blue crayons, there are 6 white crayons.
• When there are 12 white crayons, there are 16 blue crayons.

The pair of answers is 6; 16.