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Since English books are 5/7 of total books,

We can let number of English books be 5 units, and non-English books be 2 units , a total of 7 units.

60% → 60/100 = 6/10 = 3/5

So we can let number of English magazines be 3 parts, and non-English magazines be 2 parts, a total of 5 parts.

Since there are 92 English books and magazines in total, total number of non-English magazines and books = 132 - 92 = 40

From the info about non-English books, we can deduce that:

2 units + 2 parts = 40

Then 1 unit + 1 part = 20

5 units + 5 parts = 100

Total number of books and magazines = 7 units + 5 parts = 132

132 = 2 units + 5 units + 5 parts

132 = 2 units + 100

From this we can deduce that 2 units = 132 - 100 = 32

1 unit = 32 ÷ 2 = 16

a)

Number of books = 7 units = 7 x 16 = 112

b)

1 part = 20 - 1 unit = 20 - 16 = 4

Number of English magazines = 3 parts

= 3 x 4 = 12

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Is this really a P5 problem?

Solved with some algebraic manipulation, which is, to the best of my knowledge, outside of the P5 syllabus.

Alternatively, guess and check may work, but will be very time consuming, as each possible answer has to be verified and eliminated accordingly.

To use guess and check, you will have to list out a combination of multiples of 7 and multiples of 10 that can add up to 132.

Solved with some algebraic manipulation, which is, to the best of my knowledge, outside of the P5 syllabus.

Alternatively, guess and check may work, but will be very time consuming, as each possible answer has to be verified and eliminated accordingly.

To use guess and check, you will have to list out a combination of multiples of 7 and multiples of 10 that can add up to 132.

Date Posted:
3 weeks ago

Diagram/model representation :

All Books : ⬛⬛⬛⬛⬛⬛⬛

All Magazines : ⬜⬜⬜⬜⬜

Total = 132

English books : ⬛⬛⬛⬛⬛

English magazines : ⬜⬜⬜

Total for English = 92

Non-English books : ⬛⬛

Non-English magazines : ⬜⬜

Total for non-English = 132 - 92 = 40

So ⬛⬛ + ⬜⬜ = 40

Then ⬛ + ⬜ = 40 ÷ 2 = 20

Then ⬛⬛⬛⬛⬛ + ⬜⬜⬜⬜⬜ = 20 x 5 = 100

From above we know

⬛⬛⬛⬛⬛⬛⬛ +⬜⬜⬜⬜⬜ = 132

⬛⬛⬛⬛⬛ + ⬜⬜⬜⬜⬜ + ⬛⬛ = 132

100 + ⬛⬛ = 132

So ⬛⬛ = 132 - 100 = 32

⬛ = 32 ÷ 2 = 16

⬜ = 20 - 16 = 4

a) all books = 7 × ⬛ = 7 × 16 = 112

b) English magazines = 3 × ⬜ = 3 x 4 = 12

All Books : ⬛⬛⬛⬛⬛⬛⬛

All Magazines : ⬜⬜⬜⬜⬜

Total = 132

English books : ⬛⬛⬛⬛⬛

English magazines : ⬜⬜⬜

Total for English = 92

Non-English books : ⬛⬛

Non-English magazines : ⬜⬜

Total for non-English = 132 - 92 = 40

So ⬛⬛ + ⬜⬜ = 40

Then ⬛ + ⬜ = 40 ÷ 2 = 20

Then ⬛⬛⬛⬛⬛ + ⬜⬜⬜⬜⬜ = 20 x 5 = 100

From above we know

⬛⬛⬛⬛⬛⬛⬛ +⬜⬜⬜⬜⬜ = 132

⬛⬛⬛⬛⬛ + ⬜⬜⬜⬜⬜ + ⬛⬛ = 132

100 + ⬛⬛ = 132

So ⬛⬛ = 132 - 100 = 32

⬛ = 32 ÷ 2 = 16

⬜ = 20 - 16 = 4

a) all books = 7 × ⬛ = 7 × 16 = 112

b) English magazines = 3 × ⬜ = 3 x 4 = 12

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Hope this helps

Date Posted:
3 weeks ago