Question

To paint a sunset, Tran makes a shade of orange paint using 5 drops of red paint for every 8 drops of yellow paint.

If Tran uses 15 drops of red paint, how many drops of yellow paint would he need?

Math item stem image

Answer 1

24

Explanation:

The ratio for the orange color is 5:8 (5 for red, 8 for yellow)

15:5= 3 (the times the ratio was multiplied by)

so we need to multiply the i by 3 to keep the same ratio

8×3=24

Answer 2

24

Explanation:

Solve using factor of increase.

If Tran wants to make the same shade of orange, he would need to increase the yellow paint by the same factor as the red paint.

Factor = new Red ÷ old Red

= 15/5 = 3

The red paint was increased by a factor of 3.

Increase the yellow paint by a factor of 3. Multiply old Yellow by 3.

8 X 3 = 24

Therefore Tran will need 24 drops of yellow paint.

Solve using a proportion algebraically.

The ratio of yellow:red paint needs to be the same. The ratio is represented by this proportion. (Always put the missing value on top).

let y be the numbers of drops of yellow paint

`(y)/(15) = (8)/(5)`

Isolate "y" in the proportion. If you multiply both sides by 15, "y" will be isolated. (Dividing then multiplying by 15 cancels out).

`(y)/(15) = (8)/(5)`

`15*(y)/(15) = 15*(8)/(5)` Multiply both sides by 15

`(15y)/(15) = (15*8)/(5)` Combine into the numerator

`y = (15*8)/(5)` Solve the numerator

`y = (120)/(5)` Divide the top by the bottom

`y = 24` Answer

Therefore Tran will need 24 drops of yellow paint.