Question

A family-size box of laundry detergent contains 45 cups of detergent. Each load of laundry uses 0.25 cups. The family-sized box advertises that it can wash 20% more loads than the regular-sized box. How man loads of laundry can be washed with the regular-sized box?

Answer 1

150

Explanation:

45/0.25 = 180

20% more is 100+20 = 120% of the regular

120/100 × X = 180

X = 180×100/120

X = 150

Answer 2

From Regular-sized box 150 loads of laundry can be washed.

Explanation:

Given:

Contains of detergent in Family-size box = 45 cups

Each load of Laundry uses = 0.25 cups

Now Given:

The family-sized box advertises that it can wash 20% more loads than the regular-sized box.

Let the contains in regular box be 'x'.

Contains of detergents in family box is given by 20% times contains in regular box.

framing in equation form we get;

`x+(20)/(100)x=45\\`

Now taking LCM to make the denominator common we get;

`(100x)/(100)+(20x)/(100)=45\\\\(100x+20x)/(100)=45\\\\(120x)/(100)=45\\`

Multiplying both side by 100 we get;

`(120x)/(100)*100=45*100\\\\120x =4500`

Now Dividing both side by 120 we get;

`(120x)/(120)=(4500)/(120)\\\\x =37.5 \ cups`

Hence Regular box contains detergents = 37.5 cups.

Now we need to find number of loads of laundry can be washed with the regular-sized box.

So number of loads can be calculated by dividing Regular box contains detergents with Amount of detergent used by laundry for each load.

framing in equation form we get;

number of loads =
`(37.5)/(0.25) = 150 \ loads`

Hence From Regular-sized box 150 loads of laundry can be washed.