Question

What should be subtracted from 10, 12, 13, 16 so that the remaining numbers may be proportional?

• A. 3
• B. 9
• C. 4
• D. 12

Answer 1

Answer:

C. 4

Let (x) be the number to be subtracted from each of the numbers 10, 12, 13, and 16.

For the remaining numbers to be proportional:

(10-x):(12-x) = (13-x):(16-x)

So,

$\frac{10-x}{12-x}=\frac{13-x}{16-x}$

Cross-multiply:

$(10-x)(16-x)=(12-x)(13-x)$

Expand:

$160-26x+x^2 = 156-25x+x^2$

Cancel (x^2) from both sides:

$160-26x = 156-25x$
$4 = x$

Therefore,

$\boxed{4}$

Check:

After subtracting 4:

• (10-4=6)

• (12-4=8)

• (13-4=9)

• (16-4=12)

And:

6:8 = 9:12 = 3:4

$Answer: (\boxed{4}).$