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If x% of 800 = 15% of 400 + 20% of 300, then the value of x is:
12
15
18
20
15
Express percentages as fractions or use the 'Percentage Balancing' trick: 8x=(15├Ч4)+(20├Ч3), which simplifies to 8x=60+60=120. Then x=8120тАЛ=15.
x% of 800, 15% of 400, and 20% of 300.
100xтАЛ├Ч800=10015тАЛ├Ч400+10020тАЛ├Ч300
Express percentages as fractions or use the 'Percentage Balancing' trick: 8x=(15├Ч4)+(20├Ч3), which simplifies to 8x=60+60=120. Then x=8120тАЛ=15.
Many students get confused by the division by 100 on both sides and try to perform long calculations instead of canceling out the denominators (100) from all terms.
Set up the equation
Translate the percentage statements into a mathematical equation using the formula x%┬аof┬аy=100xтАЛ├Чy.
100xтАЛ├Ч800=(10015тАЛ├Ч400)+(10020тАЛ├Ч300)
Simplify both sides
Cancel the factor of 100 from all denominators to simplify the equation to 8x=(15├Ч4)+(20├Ч3).
8x=60+60
Solve for x
Add the values on the right side and divide by 8 to find the value of x.
8x=120тЯ╣x=8120тАЛ=15
B is correct because the calculation 8x=120 yields x=15.
This type of percentage balancing is highly useful in Profit and Loss and Mixture and Alligation problems where you compare weighted averages.
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