Mona and Donald fly to Rome for the weekend...

LUANDATO wrote:Mona and Donald fly to Rome for the weekend. They take cash only in notes of $10 and notes of €10. Mona carries three times the amount of euros Donald carries. She also carries as many dollars as Donald carries. The number of €10 notes they take is double the number of $10 notes they take. If Donald carries a total of 40 notes (of either $10 or €10) then what is the total number of notes (of either $10 or €10) they take?

A. 70
B. 80
C. 100
D. 120
E. 150

The OA is D.

I'm really confused by this PS question. Experts, any suggestion about how to solve it? Thanks in advance.

Call the number of dollar denominated notes Mona carries, Md.
Number of euro denominated notes Mona carries Me
Donald's dollar denominated Dd
Donald's euro De

Translate the statements using the above variables.

Me = 3De (1)
Md = Dd (2)
Me + De = 2*(Md + Dd) (3)
Dd + De = 40 (4)

Substitute (1) into left half of (3) and (2) into right half of (3):
4De = 2(Dd + Dd)

therefore 4De=4Dd > De=Dd.

Reviewing (4) above, De=Dd means each must = 20.

Substitute 20 for De back into (1) means Me = 60

Substitute 20 for Dd into (2) means Md = 20

Now all 4 variables are identified. Adding together De+Dd+Me+Md = 20+20+60+20=120, D

LUANDATO wrote:Mona and Donald fly to Rome for the weekend. They take cash only in notes of $10 and notes of €10. Mona carries three times the amount of euros Donald carries. She also carries as many dollars as Donald carries. The number of €10 notes they take is double the number of $10 notes they take. If Donald carries a total of 40 notes (of either $10 or €10) then what is the total number of notes (of either $10 or €10) they take?

A. 70
B. 80
C. 100
D. 120
E. 150

We can let the number of $10 notes Mona and Donald each carries = d since they each carry the same number of dollars.

We can let the number of €10 notes Donald carries = e, and thus the number of €10 notes Mona carries is 3e, since she carries three times the amount of euros Donald carries.

We need to determine the total number of notes they both take, i.e., the value of (d + e) + (d + 3e) = 2d + 4e.

From this we can see that 2d is the total number of $10 notes they both take, and 4e is the total number of €10 notes they both take.

We are given that the number of €10 notes they take is double the number of $10 notes. That is:

4e = 2(2d)

4e = 4d

e = d

We are also given that Donald carries a total of 40 notes (of either $10 or €10), which means that d + e = 40. However, since e = d, e and d must be each = 20. Therefore, the total number of notes they both take (or carry) is:

2d + 4e = 2(20) + 4(20) = 40 + 80 = 120

Answer: D