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Which number, when added to each of the numbers 2, 3, 11 and 13, will make the resulting numbers in proportion?
6
4
5
7
7
Use the option elimination method: plug in the values from options into the proportion. For 7: (2+7)/(3+7) = 9/10 and (11+7)/(13+7) = 18/20 = 9/10. Since 9/10 = 9/10, the answer is 7.
The numbers given are 2, 3, 11, and 13. We need to find a number x such that (2+x)/(3+x) = (11+x)/(13+x).
b+xa+xтАЛ=d+xc+xтАЛ
Use the option elimination method: plug in the values from options into the proportion. For 7: (2+7)/(3+7) = 9/10 and (11+7)/(13+7) = 18/20 = 9/10. Since 9/10 = 9/10, the answer is 7.
Students often try to solve the quadratic equation (2+x)(13+x)=(3+x)(11+x) manually, which leads to time-consuming expansion and potential algebraic errors.
Set up the proportion equation
Let the number to be added be x. The condition for proportion is written as:
3+x2+xтАЛ=13+x11+xтАЛ
Cross-multiply and expand
Cross-multiplying gives (2+x)(13+x)=(3+x)(11+x). Expanding both sides:
26+15x+x2=33+14x+x2
Simplify and solve for x
Cancel x2 from both sides and isolate x by shifting terms:
15xтИТ14x=33тИТ26тЯ╣x=7
D is correct because substituting x=7 into the ratios results in 9/10 for both pairs, confirming they are in proportion.
This type of problem appears frequently in Partnership and Mixture problems where you check for balanced ratios to determine unknown quantities quickly.
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