Laqueta has three times as many quarters as Pablo if they each spend $.50 Laqueta will have five times as many quarters as Pablo how many quarters do Laqueta and Pablo have now?
Laqueta's number of quarters are expressed in terms of how many relative to Pablo's number, so let's call Pablo's original number of quarters, P. Let's express Laqueta's original number of quarters as L.
P: # of quarters that Pablo originally had
L: # of quarters that Laqueta originally had
The number of quarters that Laqueta has can be expressed as 3P.
L = 3P
$0.50 is fifty cents or two quarters. If you spend two quarters, you will have two fewer than you did before you spent them.
After each spends 50 cents, Pablo has (P – 2) quarters and Laqueta has (3P – 2) quarters. We also know that Laqueta's new amount (3P – 2) is five times as much as Pablo's new amount (P – 2); we can create an equation to express that:
3P – 2 = 5(P – 2)
Solve this equation for P.
3P – 2 = 5P – 10
3P – 3P – 2 = 5P – 3P – 10
– 2 = 2P – 10
–2 + 10 = 2P – 10 + 10
8 = 2P
Divide by 2 to get:
4 = P
Now we know that Pablo ORIGINALLY HAD four quarters. Now we need to calculate how many he has after spending two quarters ($0.50). He would have (4 – 2) or 2 quarters remaining.
Laqueta would (3P – 2) quarters or (3[4] – 2) or (12 – 2) or 10 quarters ($2.50).
Let's check our work. If Pablo had 4 quarters at the beginning, then did Laqueta have 3 times as many?? Well, she had 3P or 3(4), so she had 12 quarters and that is 3 times as many as 4.
At the end, Pablo had 2 quarters and Laqueta had 10, and 10 is five times 2. So we did well!!
