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If Mason is now twice as old as Gunther was 10 years ago, an
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14 Jun 2018, 14:22
14 Jun 2018, 14:22
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86% (01:32) correct
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If Mason is now twice as old as Gunther was 10 years ago, and G is Gunther’s current age in years, which of the following represents the sum of Mason and Gunther’s ages 4 years from now?
(A) \(\frac{3G}{2}+ 3\)
(B) 3G + 28
(C) 3G – 12
(D) 8 – G
(E)\(14 – \frac{3G}{2}\)
(A) \(\frac{3G}{2}+ 3\)
(B) 3G + 28
(C) 3G – 12
(D) 8 – G
(E)\(14 – \frac{3G}{2}\)
Re: If Mason is now twice as old as Gunther was 10 years ago, an
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15 Jun 2018, 08:08
15 Jun 2018, 08:08
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sandy wrote:
If Mason is now twice as old as Gunther was 10 years ago, and G is Gunther’s current age in years, which of the following represents the sum of Mason and Gunther’s ages 4 years from now?
(A) \(\frac{3G}{2}+ 3\)
(B) 3G + 28
(C) 3G – 12
(D) 8 – G
(E)\(14 – \frac{3G}{2}\)
(A) \(\frac{3G}{2}+ 3\)
(B) 3G + 28
(C) 3G – 12
(D) 8 – G
(E)\(14 – \frac{3G}{2}\)
Correct me if my solution is wrong.
Mason is now twice as old as Gunther was 10 years ago => M = 2(G-10) = 2G-20
To find 'sum of Mason and Gunther’s ages 4 years from now', M+4 = 2G-20+4 =>2G-16 and G in another 4 years will G+4.
Sum of both 2G-16 + G + 4 => 3G - 12.
C.
Re: If Mason is now twice as old as Gunther was 10 years ago, an
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05 Jul 2018, 03:04
05 Jul 2018, 03:04
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Expert Reply
Explanation
The sum of Mason and Gunther’s ages 4 years from now requires adding 4 to both ages.
The question asks for the following, the sum of Mason and Gunther’s ages 4 years from now:
\((M + 4) + (G + 4) = ?\)
\(M + G + 8 = ?\)
Since Mason is twice as old as Gunther was 10 years ago, put (G – 10) in parentheses and build the second equation from there (the parentheses are crucial):
\(M = 2(G - 10)\)
\(M = 2G - 20\)
Note that the answer choices ask for the sum of the ages 4 years from now, in terms of G, so substitute for M (the variable you substitute for is the one that drops out).
Substituting from the second equation into the first:
\((2G - 20) + G + 8 = ?\)
3G - 12 = ?
This matches choice C.
Alternatively, you could write the second equation, M = 2(G – 10), and then come up with two values that “work” in this equation for M and G. The easiest way to do this is to make up G, which will then tell you M. For instance, set G = 12 (use any number you want, as long as it’s over 10, since the
problem strongly implies that Gunther has been alive for more than 10 years):
\(M = 2(12 - 10)\)
\(M = 4\)
If Gunther is 12, then Mason is 4. In four years, they will be 16 and 8, respectively. Add these together to get 24.
Now, plug G = 12 into each answer choice to see which yields the correct answer (for this example), 24. Only choice (C) works.
The sum of Mason and Gunther’s ages 4 years from now requires adding 4 to both ages.
The question asks for the following, the sum of Mason and Gunther’s ages 4 years from now:
\((M + 4) + (G + 4) = ?\)
\(M + G + 8 = ?\)
Since Mason is twice as old as Gunther was 10 years ago, put (G – 10) in parentheses and build the second equation from there (the parentheses are crucial):
\(M = 2(G - 10)\)
\(M = 2G - 20\)
Note that the answer choices ask for the sum of the ages 4 years from now, in terms of G, so substitute for M (the variable you substitute for is the one that drops out).
Substituting from the second equation into the first:
\((2G - 20) + G + 8 = ?\)
3G - 12 = ?
This matches choice C.
Alternatively, you could write the second equation, M = 2(G – 10), and then come up with two values that “work” in this equation for M and G. The easiest way to do this is to make up G, which will then tell you M. For instance, set G = 12 (use any number you want, as long as it’s over 10, since the
problem strongly implies that Gunther has been alive for more than 10 years):
\(M = 2(12 - 10)\)
\(M = 4\)
If Gunther is 12, then Mason is 4. In four years, they will be 16 and 8, respectively. Add these together to get 24.
Now, plug G = 12 into each answer choice to see which yields the correct answer (for this example), 24. Only choice (C) works.
