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# Lou has three daughters: Wen, Mildred, and Tyla. Three years

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GRE Prep Club Legend
Joined: 07 Jun 2014
Posts: 4856
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
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Kudos [?]: 1737 [0], given: 397

Lou has three daughters: Wen, Mildred, and Tyla. Three years [#permalink]  14 Jun 2018, 14:25
Expert's post
00:00

Question Stats:

66% (04:40) correct 33% (03:42) wrong based on 3 sessions
Lou has three daughters: Wen, Mildred, and Tyla. Three years ago, when Lou was twice as old as Tyla, he was 30 years older than Mildred. Now, he is 47 years older than Wen. In 4 years, Wen will be half as old as Tyla. What is the sum of the current ages of Lou and his three daughters?

(A) 138
(B) 144
(C) 154
(D) 166
(E) 181
[Reveal] Spoiler: OA

_________________

Sandy
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GRE Prep Club Legend
Joined: 07 Jun 2014
Posts: 4856
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 102

Kudos [?]: 1737 [0], given: 397

Re: Lou has three daughters: Wen, Mildred, and Tyla. Three years [#permalink]  05 Jul 2018, 03:21
Expert's post
Explanation

The key to this tricky-sounding problem is setting up variables correctly and ensuring that you subtract or add appropriately for these variables when representing their ages at different points in time:

L = Lou’s age now
W = Wen’s age now
M = Mildred’s age now
T = Tyla’s age now

Two equations come from the second sentence of the problem:

Equation 1: $$(L - 3) = 2(T - 3)$$
Equation 2: $$(L - 3) = (M - 3) + 30$$

Another two equations come from the third sentence of the problem:

Equation 3: $$L = W + 47$$
Equation 4: $$(W + 4) =\frac{T+4}{2}$$

In order to solve this problem effectively, look for ways to get two of the equations to have the same two variables in them. If you have two equations with only two variables, you can solve for both of those variables. Equation 4 has a W and a T; the only other equation with a T is Equation 1. If you substitute the L in Equation 1 with the W from Equation 3, you will have two equations with just W’s and T’s.

Equation 1: $$(L - 3) = 2(T - 3)$$

$$(W + 47) – 3 = 2(T - 3)$$

$$W + 44 = 2T - 6$$

$$W + 50 = 2T$$

Equation 4: $$(W + 4) =\frac{T+4}{2}$$

$$2W + 8 = T + 4$$

$$2W + 4 = T$$

Now combine the equations to solve for W.

$$W + 50 = 2(2W + 4)$$

$$W + 50 = 4W + 8$$

$$W + 42 = 4W$$

$$42 = 3W$$

$$14 = W$$

Now that you know Wen’s age, you can solve for the rest.

Equation 3: $$L = W + 47$$
$$L = 14 + 47$$
$$L = 61$$

Equation 1: $$(L - 3) = 2(T - 3)$$

$$(61 - 3) = 2(T - 3)$$

$$58 = 2T - 6$$

$$64 = 2T$$

$$32 = T$$

Equation 2: $$(L - 3) = (M - 3) + 30$$

$$(61 - 3) = (M - 3) + 30$$

$$58 = M + 27$$

$$31 = M$$

Now that you know that L = 61, W = 14, M = 31, and T = 32, sum them to find the answer:

$$61 + 14 + 31 + 32 = 138$$
_________________

Sandy
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Re: Lou has three daughters: Wen, Mildred, and Tyla. Three years   [#permalink] 05 Jul 2018, 03:21
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