Question

7) The ratio of lipsticks to eye shadow in my makeup bag is 1:9. The ratio of eye shadow to mascara is 3:2. Given that I have 3 more eye shadows than mascaras, how many lipsticks do I have?

Answer 1

By solving the equations derived from the given ratios (lipsticks to eye shadows as 1:9, and eye shadows to mascaras as 3:2) and the additional information (3 more eye shadows than mascaras), we conclude that there is 1 lipstick in the makeup bag.

Step-by-step explanation:

We are given two ratios: the ratio of lipsticks to eye shadows is 1:9, and the ratio of eye shadows to mascaras is 3:2. We also know that there are three more eye shadows than mascaras. To find out how many lipsticks there are, we need to solve for the number of mascaras first, and then use that to find the number of lipsticks.

Let's assume that the number of mascaras is x. Then according to the ratio of eye shadows to mascaras (3:2), the number of eye shadows will be 3÷ 2 times x which simplifies to 1.5x. But we are told there are 3 more eye shadows than mascaras, so the equation can be written as 1.5x = x + 3.

Solving the equation 1.5x = x + 3, we get:

• 1.5x - x = 3
• 0.5x = 3
• x = 3 ÷ 0.5
• x = 6 (number of mascaras)

Thus, the number of eye shadows is 1.5x = 1.5 × 6 = 9. Going back to the ratio of lipsticks to eye shadows (1:9), we can now find the number of lipsticks as follows:

• If 9 eye shadows correspond to 1 lipstick,
• Then 1 eye shadow would correspond to 1÷ 9 of a lipstick,
• So, 9 eye shadows correspond to 9 × (1÷ 9) = 1 lipstick.

Hence, there is 1 lipstick in the makeup bag.

Answer 2

1

Step-by-step explanation:

If you have 1 lipstick, then you have 9 eye shadows, at the same time, if you have 3 eye shadows, you have 2 mascaras. Since it's stated from the first part that you have 9 eye shadows, then going by the ratio, you must have 6 mascaras.

Final part says if there are 3 more eye shadows than mascaras, how many lipsticks have you.

This is quite straightforward, because from the relation I've established up ahead, we have 9 eye shadows and 6 mascaras. And 9 is 3 more than 6. Essentially, this means that the number of lipsticks will remain 1