Question

A group of students were surveyed about their hat choices for the spirit week at their college. 60% of them converged on solid-color hats, 22% of them wanted hats with stripes and the rest of them liked star hats. The anticipation says that there are 1800 students in the college and each will buy one hat. From the above table, calculate the number of solid-colored hats Wilhelmina and Alexandra are responsible for knitting, if the ratios in the table remain constant for Spirit Week hat production.

	Scarves	Pairs of Mittens	Hats
Wilhelmina	7	2	24
Emanuel	8	2	9
Jose Raul	3	4	18
Alexandra	15	1	9
Total	33	9	60

Answer 1

Hint: Based on the given table, we can find how many hats are responsible by Wilhelmina and Alexandra. By this we can find how many solid colored hats are there. We need to multiply this solid colored hats will yield the number that Wilhelmina and Alexandra will knit.

Complete step-by-step answer:
Given, a group of students were surveyed about their hat choices for the spirit week at their college.
60% of them converged on solid-color hats.
22% of them wanted hats with stripes.
Rest of them liked star hats.
The anticipation says that there are 1800 students in the college and each will buy one hat.
According to the table Wilhelmina will be responsible for $\dfrac{{24}}{{60}}$ of the hats, and Alexandra will knot $\dfrac{9}{{60}}$ of them.
The knitting club needs to knit 1800 hats total, 60% of which should be solid colored per the survey results.
This means that $0.6 \times 1800 = 1080$hats should be solid-colored.
Add together the fraction for Wilhelmina and Alexandra to get$\dfrac{{33}}{{60}}$
Multiplying this by the totals number of solid coloured hats will yield the number that Wilhelmina and Alexandra will knit:$\dfrac{{33}}{{60}} \times 1080 = 594$
Therefore, 594 number of solid-colored hats will Wilhelmina and Alexandra are responsible for knitting, if the ratios in the table remain constant for Spirit Week hat production.

Note: We can do this problem in a different way that is, we can calculate the fraction of hats responsible by others without including Wilhelmina and Alexandra then the obtained fraction is multiplied by the solid colored hats count. This will be deducted from the total 1800 hats.