BTGModeratorVI wrote: ↑

Thu Dec 03, 2020 2:41 pm

Beth, Naomi, and Juan raised a total of $55 for charity. Naomi raised $5 less than Juan, and Juan raised twice as much as Beth. How much did Beth raise?

A.  $9
B. $10
C. $12
D. $13
E. $15

Answer: C
Source: official guide

Solution:

Let B, N and J be the amount of money Beth, Naomi, and Juan raised, respectively. We can create the equations:

B + N + J = 55

N = J - 5

and

J = 2B

Since J = 2B, N = 2B - 5. Substituting these quantities in the first equation, we have:

B + 2B - 5 + 2B = 55

5B = 60

B = 12

Answer: C

BTGModeratorVI wrote: ↑

Thu Dec 03, 2020 2:41 pm

Beth, Naomi, and Juan raised a total of $55 for charity. Naomi raised $5 less than Juan, and Juan raised twice as much as Beth. How much did Beth raise?

A.  $9
B. $10
C. $12
D. $13
E. $15

Answer: C
Source: official guide

Let B = the amount that Beth raised

Juan raised twice as much as Beth
So, 2B = the amount Juan raised

Naomi raised $5 less than Juan
So, 2B - 5 = amount Naomi raised

Beth, Naomi, and Juan raised a total of $55
In other words: (Beth's amount) + (Naomi's amount) + (Juan's amount) = 55
Substitute to get: B + (2B - 5) + 2B = 55
Simplify: 5B - 5 = 55
Add 5 to both sides of the equation: 5B = 60
Divide both sides by 5 to get: B = 12

In other words, Beth raised $12

Answer: C

Cheers,
Brent