Question

Timothy, Laurence and Mike went to a bookstore to buy some books. The ratio of the number of books bought by Laurence and Mike were 2: 7. Timothy and Laurence bought a total of 20 books while Timothy and Mike bought a total of 35 books. How many books did Timothy buy?

Answer 1

`\mbox{\large \textsf{Timothy bought 14 books}}`

Explanation:

Let's use first letters of names to represent the number of books bought by that person. This makes it easier to explain.

Therefore, the books bought by each of the three persons are T(imothy), L(aurence) and M(ike)

We will now convert each of the word description into math equations and solve

We are given that the ratio of the number of books bought by Laurence and Mike were 2: 7

We can write this as:

`(L)/(M) = (2)/(7)\\\\`

Multiplying both sides by M:

`L = (2)/(7)M\cdots\cdots(1)`

Timothy and Laurence bought a total of 20 books can be represented as

`T + L = 20\cdots\cdots(2)`

Timothy and Mike bought a total of 35 books can be represented as

`T + M = 35\cdots\cdots(3)`

Eq (3) - Eq (2):


`T + M - (T + L) = 35 - 20\\\\T + M - T - L = 15\\\\M - L = 15 \cdots\cdots (4)`

Substituting for
`\displaystyle L = (2)/(7)M` from equation (1) into equation (4) we get

`M - (2)/(7)M = 15\\\\(5)/(7)M = 15\\\\M = (7)/(5) * 15\\\\M = 21\\\\`

Given
`\displaystyle M = 21` using equation (3),
`\displaystyle T + M = 35` we get


`T + 21 = 35\\\\T = 35 - 21\\\\\textrm{or}\\\\T = 14`(Answer)

If we wanted to find out how many books Laurence bought use Eq(1)

`L = (2)/(7)M\\\\L = (2)/(7) * 21\\\\L = 6\\\\`