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If 85% of a number is added to 24, then the result is the same number. 75% of the same number is:
90
160
120
150
120
If adding a percentage to reach 100% equals 24, then the missing 15% (100% - 85%) must be 24. Find 100% (24/0.15=160) and then calculate 75% of 160.
85% of a number is added to 24 results in the number itself.
0.85x+24=x
If adding a percentage to reach 100% equals 24, then the missing 15% (100% - 85%) must be 24. Find 100% (24/0.15=160) and then calculate 75% of 160.
Confusing the number itself with 75% of the number; ensure you calculate 0.75x at the end.
Set up the algebraic equation
Let the number be x. The problem states that 85% of x added to 24 equals x.
0.85x+24=x
Solve for x
Subtract 0.85x from both sides to isolate the constant term.
24=xтИТ0.85x=0.15x
Calculate the value of x
Divide 24 by 0.15 to find the number.
x=0.1524тАЛ=152400тАЛ=160
Calculate 75% of the number
Now, find 75% (or 3/4) of 160.
0.75├Ч160=43тАЛ├Ч160=3├Ч40=120
C is correct because the number is 160, and 75% of 160 is 120.
This type of percentage-deficit question is common in interest and profit/loss problems where finding the base value (100%) is the first critical step.
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