Question

Benny and Cuppy volunteered to sort books in the library. The total number of English and Chinese books sorted was 365. The total number of English and Math books sorted was 302. The number of Math books was 4 /7 of the number of Chinese books. How many English books were there?

Answer 1

Let's call the number of English books "E", the number of Chinese books "C", and the number of Math books "M".

We know that:

E + C = 365 (Equation 1)

E + M = 302 (Equation 2)

M = 4/7 C (Equation 3)

We can solve for one variable in terms of the others and substitute into the other equations.

Let's solve Equation 3 for C:

M = 4/7 C

C = 7/4 M

Now we can substitute this into Equation 1:

E + C = 365

E + (7/4 M) = 365

And into Equation 2:

E + M = 302

E + M = 302

Now we have two equations with two variables, E and M. We can solve for one of them and then use that to solve for the other.

Let's subtract Equation 2 from Equation 1:

E + (7/4 M) = 365

- E - M = -302

-----------------

(3/4 M) = 63

Multiply both sides by 4/3:

M = 84

Now we can use Equation 2 to solve for E:

E + M = 302

E + 84 = 302

E = 218

So there were 218 English books.