I need help solving word problems

Question

caleb, lime, and ava shared 240 stickers. Caleb received twice as many stickers as Lime. Lime received 3 times as many as Ava. How many stickers did Caleb receive?

Answer 1

Hello, thank you for taking the time to post your question!

The key on this type of question is to start by defining the relationship between the variables based on the information given. So in this one we know that there are 240 stickers total, so A + L + C = 240

Then we have Lime received 3 times as many as Ava, so that is

L = 3A

And Caleb received twice as many as Lime:

C = 2L = 2(3A) = 6A

Substituting it into the original equation gives

A + 3A + 6A = 240

10A = 240

A = 24

So Ava received 24 stickers, meaning that Caleb received

C = 6(24) = 144 stickers

I hope that helps get you moving in the right direction! Feel free to reach out if you have any additional questions beyond that :)

Answer 2

We can set Caleb as C = 2L, L for Lime and C for Caleb.

Since L received 3 times as many as Ava, we can write L = 3A

And now we have to write A in terms of L (since the first two monomials, or terms, are written with an L)- Divide both sides by 3, that gives us A = L/3

Let's add all the monomials together, that gives us:

2L + L + L/3 = 240

Next step would be to write all three terms with the same LCD (Least Common Denominator). The LCD is 3, so that gives us:

(6L + 3L + L)/3 = 240. Multiply both sides by 3, that gives us: 10L = 720. Divide both sides by 10, that gives us L = 72.

We're looking for Caleb, and remember C for Caleb = 2 L. So we plug L (72) into 2L. That gives us 72 times 2 = 144!

Answer 3

In total, there are 240 stickers.

We'll represent the number of stickers each received like this: Caleb with a, Lime with b, and Ava with c.

Caleb received twice as many stickers as Lime.

We can write this as:

a = 2 * b

Lime received 3 times as many as Ava.

We can write this as:

b = 3 * c

We also know that they shared all 240 of the stickers, which means that the sum of all of their individual stickers equals that much.

We can write this as:

a + b + c = 240

In order to figure out how many stickers Caleb has, we have to isolate his variable, a.

Let's start out by getting b in terms of a.

We'll start with what we know about the two:

a = 2 * b

Divide both sides by 2:

a / 2 = b

Now we can plug that into our big equation:

a + b + c = 240

We now know b = a / 2, so we can substitute b with a / 2:

a + (a / 2) + c = 240

Now let's get c in terms of a.

We'll start with what we know about c:

b = 3 * c

We don't want b in there, so let's substitute b with a / 2 again:

a / 2 = 3 * c

Divide both sides by the 3:

a / 6 = c

Now we can plug that into our big equation:

a + (a / 2) + c = 240

We now know c = a / 6, so we can substitute c with a / 6:

a + (a / 2) + (a / 6) = 240

In order to get rid of the denominators, lets multiply both sides by 6:

6 * (a + a / 2 + a / 6) = 6 * (240)

Distribute the 6 between the factors:

6a + 6a/2 + 6a/6 = 1440

Reduce where necessary:

6a + 3a + a = 1440

Combine like terms:

10a = 1440

Divide out the 10:

a = 144

So now we know that Caleb has 144 out of the original 240 stickers.

Let's check this against what we started with to make sure our math was correct.

We'll start with our original equation in the last section:

a + (a / 2) + (a / 6) = 240

We'll substitute in 144 for Caleb's sticker count (a):

144 + 144 / 2 + 144 / 6 = 240

And evaluate:

144 + 72 + 24 = 240

240 = 240

Yes! Our answer is correct and verified.