Question

by what percent will the product of 2 number decrease if one of the is decreased by 25% and the other by 50%

Answer 1

Answer:

The product has decreased by 1 - 0.375, or 0.625, or 62.5%

Step-by-step explanation:

well, let's say the numbers are "a" and "b"

so a * b = ab

ok... now, if we reduce "a" by 25%, that means the new size is just 75% of the old one, how much is 75% of a? well, (75/100) * a, or 0.75a

now let's reduce "b" by 50%, that means the new size is 50% or half, how much is 50% of b? well (50/100)*b, or 0.5b

\begin{gathered}\bf \begin{cases} a\cdot b\implies ab\\ 0.75a\cdot 0.5b\\ \qquad 0.75\cdot 0.5ab\\ \qquad 0.375ab \end{cases}\end{gathered}

⎩

⎪

⎪

⎪

⎪

⎨

⎪

⎪

⎪

⎪

⎧

a⋅b⟹ab

0.75a⋅0.5b

0.75⋅0.5ab

0.375ab

now, the new size of "ab" is just 0.375ab... well, let's revert the decimal format by simply multiplying by 100

0.375 * 100, is 37.5%

the new size of "ab" is just 37.5% of the original "ab"

it decreased by 100 - 37.5 or 62.5%