Elsa, Carlos, and Bob have a total of $79 in there wallets. Bob has 2 times what Carlos has. Carlos has $5 more than Elsa. How much do they have in their wallets?

Answer 1

This type of problem can be very fun once you know how to set it up!

First, assign a letter for each of the players. E = Elsa, C = Carlos, B = Bob

Then write down in math terms exactly what you read: BTW, verbs (is, are, was, were, has, have, had) are your relation symbols, mainly =.

They have a total of $79, so write down: E + C + B = 79.

Bob has 2 times as much as Carlos: B = (2C)

Carlos has $5 more than Elsa: C = E + 5, which also means Elsa has $5 less than Carlos: E = (C - 5)

So now, we can substitute what we know about each person so that we have only one variable or letter to find. Since I know that B is related to C and E is related to C, we can substitute the C phrases into the first equation:

E + C + B = 79, so

(C - 5) + C + (2C) = 79

Now we collect like terms and solve for C:

C + C + 2C - 5 = 79

4C - 5 = 79

+ 5 to both sides: 4C = 84

divide 4 to both sides: C = 21

So now we know that Carlos has $ 21.

Since Bob has 2 times the amount as Carlos, he has $42.

And since Elsa has 5 less than Carlos, she has $16.

Now, we will know if we have the right amount for each person if we add them together and get $79.

Check: 21 + 42 + 16 = 79!!

Review of the steps:

Assign labels for the people or things.

Write a working equation.

Write relationship equations.

Substitute the relationship equations into the working equation.

Solve for 1 variable.

Go back to the relationship equations to find the other variable quantities or values.

Check by plugging the values into the working equation.

I hope this helps. BTW, you use this same process to solve age problems, geometry problems, and many other problems with multiple components or variables.

Have fun!!

Sue H.

Answer 2

Let's start with Elsa's amount since we don't know anything about how much she has. We'll call Elsa's amount "x." We know that Carlos has $5 more than Elsa, so we'll say that Carlos's amount is $5 + x. We know that Bob has 2 times as much as Carlos, so we'll say that Bob's amount is 2($5 + x). We also know that if we add all of their amounts together, we will get a total of $79. We want our problem to say:

Elsa's amount + Carlos's amount + Bob's amount = $79

Here's how our problem will look:

x + ($5 + x) + 2($5 + x) = $79.

Now all you must do is solve.

x + $5 + x + $10 + 2x = $79

4x + $15 = $79

4x = $64

x = $16

Remember that we said that Elsa's amount was x? Now we know that Elsa's wallet has $16. Carlos has $5 more than Elsa. $16 + $5 = $21. Carlos has $21 in his wallet. Bob has 2 times what Carlos has. 2 x $21 = $42. Bob has $42 in his wallet.