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Beth is 12 years younger than Alan. In 20 years, Beth will b
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14 Jun 2018, 14:29
14 Jun 2018, 14:29
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Question Stats:
85% (01:25) correct
14% (01:46) wrong based on 41 sessions
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Beth is 12 years younger than Alan. In 20 years, Beth will be 80% of Alan’s age. How old is Beth now?
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28
Re: Beth is 12 years younger than Alan. In 20 years, Beth will b
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15 Jun 2018, 01:25
15 Jun 2018, 01:25
B+12=A
B+20=0.8(A+20)
B+20=0.8(B+12+20)
B+20=0.8B+25.6
B=28
B+20=0.8(A+20)
B+20=0.8(B+12+20)
B+20=0.8B+25.6
B=28
Re: Beth is 12 years younger than Alan. In 20 years, Beth will b
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05 Jul 2018, 01:50
05 Jul 2018, 01:50
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Explanation
Since Beth is 12 years younger than Alan, you can write:
\(B = A - 12\)
To translate “in 20 years, Beth will be 80% of Alan’s age,” make sure that Beth becomes B + 20 and Alan becomes A + 20 (if you will be doing other operations to these values, put parentheses around them to make sure the rules of PEMDAS are not violated):
\(B + 20 = 0.8(A + 20)\)
\(B + 20 = 0.8A + 16\)
\(B + 4 = 0.8A\)
Since the first equation is already solved for B, plug (A – 12) into the simplified version of the second equation in place of B:
\(B + 4 = 0.8A\)
\((A - 12) + = 0.8A\)
\(A - 8 = 0.8A\)
\(0.2A - 8 = 0\)
\(0.2A = 8\)
\(A = 40\)
Alan is 40. Since B = A – 12, Beth is 28.
Check the answer. In 20 years, Beth will be 48 and Alan will be 60, and it is true that 48 is 80% of 60.
Hence the answer is 28
Since Beth is 12 years younger than Alan, you can write:
\(B = A - 12\)
To translate “in 20 years, Beth will be 80% of Alan’s age,” make sure that Beth becomes B + 20 and Alan becomes A + 20 (if you will be doing other operations to these values, put parentheses around them to make sure the rules of PEMDAS are not violated):
\(B + 20 = 0.8(A + 20)\)
\(B + 20 = 0.8A + 16\)
\(B + 4 = 0.8A\)
Since the first equation is already solved for B, plug (A – 12) into the simplified version of the second equation in place of B:
\(B + 4 = 0.8A\)
\((A - 12) + = 0.8A\)
\(A - 8 = 0.8A\)
\(0.2A - 8 = 0\)
\(0.2A = 8\)
\(A = 40\)
Alan is 40. Since B = A – 12, Beth is 28.
Check the answer. In 20 years, Beth will be 48 and Alan will be 60, and it is true that 48 is 80% of 60.
Hence the answer is 28
