Answer:
Marcus can make 12 packages, with 2 toothbrushes and 3 bars of soap in each package.
Step-by-step explanation:
For all the packages to be identical, they must all contain the same numbers of soaps and the same nuber of toothbrushes.
The ratior of soaps to brushes is 36/24 = 3/2
He could make 24 packages, each with 1 tootbrush and (3/2) bars of soap.
Assuming he is not going to cut soap bars in half, that is no good.
To make the numbers of individual items come out as integers, the smallest number he can multiply them by is the denominator on the (3/2) bar of soap. That would be a 2.
So he can makes packages with toothbrushes = Â Â 2 x 1 =2
                        and soap bars   = 3/2 x 2 = 3
He can put 5 items in each package - 3 soap bars and 2 toothbrushes.
That means he makes 12 packages.
The greatest number of packages is 12 with 2 toothbrushes and 3 soap bars in each package.
It is given that the Marcus has 36 bars and 24 toothbrushes and wants to arrange the items so the packages are identical.
It is required to find the greatest number of packages that Marcus can make using all the soap and toothbrushes.
Fraction number consists of two parts one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called denominator.
Marcus has number of bars of soap = 36 Â and
Number of tooothbrush = 24
The ratio of soap bars to toothbrushes = 36:24 Â or
= 3:2
It meanse Marcus can make 24 packets with [tex]\frac{3}{2}[/tex] soap bars and toothbrush
Because there are 24 toothbrushes but the number of bars can not be in fraction so multiply by 2 on denominator, we get:
Number of toothbrushes = 2×1 = 2
Number of soap bars = [tex]\frac{3}{2}[/tex] ×2 = 3
Now he can make total 12 packets with 2 toothbrushes and 3 soap bars.
Sum of toothbrushes and soap bars = 24+36 = 40
Number of soap bars and toothbrush in each packet = 2+3 = 5
Number of packages= [tex]\frac{60}{5}[/tex] = 12
Thus, the greatest number of packages is 12 with 2 toothbrushes and 3 soap bars.
Learn more about the fraction here:
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