Question

There are 40 children in a classroom and n of them do not wear spectacles. (4)/(5) of the boys and (2)/(3) of the girls wear spectacles. Express the number of boys who wear spectacles in terms of n.

Answer 1

9514 1404 393

Answer:

b = 80 -6n . . . . boys who wear spectacles

Explanation:

We know the ratio of boys who wear spectacles to those who don't is ...

(4/5) : (1 -4/5) = 4 : 1

If we let b represent the number of boys who wear spectacles, then the number who don't is b/4. Then total number of boys is then b +b/4 = 5b/4. The number of girls in the classroom is this number less than 40.

Let's define a few groups:

• boys who wear spectacles: b
• boys who do not wear spectacles: b/4
• girls who wear spectacles: (2/3)(40 -5b/4)
• girls who do not wear spectacles (1/3)(40 -5b/4)

Then the total of children who do not wear spectacles is ...

n = b/4 +(1/3)(40 -5b/4)

12n = 3b +(160 -5b) = 160 -2b . . . . multiply by 12

2b = 160 -12n . . . . . . . . . . . . . add 2b-12n

b = 80 -6n . . . . the desired relation, b = boys who wear spectacles

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Additional comment

The only values of n that make sense in this context are {8, 10, 12}, corresponding to {0, 15, 30} total girls and {40, 25, 10} total boys.