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Enya had a total of 280 blue and green beads. She gave away 20 blue and 3/5 of the green beads. After that, the ratio of the number of blue beads to the number of green beads left was 1 : 10. How many beads did Enya have in the end?​

User Phylis
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1 Answer

3 votes

Answer:

Explanation:

Let's start by figuring out how many green beads Enya had before giving some away.

Let g be the number of green beads Enya had initially, and let b be the number of blue beads. Then we know:

g + b = 280 (the total number of beads)

After giving away 3/5 of the green beads and 20 blue beads, Enya had g' green beads and b' blue beads left. We can set up two more equations:

g' = 2/5 g (Enya gave away 3/5 of the green beads, so she has 2/5 left)

b' = b - 20 (Enya gave away 20 blue beads)

We also know that the ratio of blue beads to green beads left is 1:10, which means:

b' / g' = 1/10

Substituting the expressions for g', b', and b from the earlier equations, we get:

(b - 20) / (2/5 g) = 1/10

Simplifying this equation, we get:

b - 20 = g/4

Now we have two equations with two variables:

g + b = 280

b - 20 = g/4

We can solve for g in the second equation:

g = 4(b - 20)

Substituting this expression for g into the first equation, we get:

4(b - 20) + b = 280

Simplifying and solving for b, we get:

5b = 360

b = 72

So Enya had 72 blue beads initially. We can use this to find the initial number of green beads:

g + 72 = 280

g = 208

Enya had 208 green beads initially.

After giving away 20 blue beads and 3/5 of the green beads, she had:

g' = 2/5 * 208 = 83

b' = 72 - 20 = 52

So Enya had a total of 83 + 52 = 135 beads left in the end.

User Jhonatan Sabadi
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