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Math  /  Numbers & Operations

QuestionSolve mentally. (NO WORK TO SHOW) A color called Passion Pink is made by mixing red paint and white paint in a ratio of 2 to 7 . How many drops of white paint do you need:
S If you use 20 drops of red paint? L If you use 40 drops of red paint? T If you use 3 drops of red paint?

Studdy Solution

STEP 1

1. The mixing ratio of red paint to white paint is 2:7.
2. The ratio remains constant regardless of the amount of red paint used.
3. We need to find the number of drops of white paint for given amounts of red paint.

STEP 2

1. Establish the relationship between the red and white paint based on the given ratio.
2. Calculate the drops of white paint for each given amount of red paint.

STEP 3

Establish the relationship between the red and white paint in terms of the ratio.
Given the ratio 2:7, for every 2 drops of red paint, there are 7 drops of white paint.

STEP 4

Calculate the drops of white paint for 20 drops of red paint.
Using the ratio 2:7: 7 drops of white paint2 drops of red paint=x drops of white paint20 drops of red paint\frac{7 \text{ drops of white paint}}{2 \text{ drops of red paint}} = \frac{x \text{ drops of white paint}}{20 \text{ drops of red paint}}
Solving for xx: x=72×20=70 drops of white paintx = \frac{7}{2} \times 20 = 70 \text{ drops of white paint}

STEP 5

Calculate the drops of white paint for 40 drops of red paint.
Using the ratio 2:7: 7 drops of white paint2 drops of red paint=x drops of white paint40 drops of red paint\frac{7 \text{ drops of white paint}}{2 \text{ drops of red paint}} = \frac{x \text{ drops of white paint}}{40 \text{ drops of red paint}}
Solving for xx: x=72×40=140 drops of white paintx = \frac{7}{2} \times 40 = 140 \text{ drops of white paint}

STEP 6

Calculate the drops of white paint for 3 drops of red paint.
Using the ratio 2:7: 7 drops of white paint2 drops of red paint=x drops of white paint3 drops of red paint\frac{7 \text{ drops of white paint}}{2 \text{ drops of red paint}} = \frac{x \text{ drops of white paint}}{3 \text{ drops of red paint}}
Solving for xx: x=72×3=10.5 drops of white paintx = \frac{7}{2} \times 3 = 10.5 \text{ drops of white paint}
The solutions are: S = 70 drops of white paint, L = 140 drops of white paint, T = 10.5 drops of white paint.

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