GCSE OCR Maths BODMAS: 7 (a) Divide 72 in the ratio 4

7 (a) Divide 72 in the ratio 4 : 5 - OCR - GCSE Maths - Question 7 - 2020 - Paper 1

Question 7

7 (a) Divide 72 in the ratio 4 : 5. (b) In one year, Clara and Dave borrowed books from a library in the ratio 3 : 7. Dave borrowed 35 books. Work out the number ... show full transcript

Worked Solution & Example Answer:7 (a) Divide 72 in the ratio 4 : 5 - OCR - GCSE Maths - Question 7 - 2020 - Paper 1

Step 1

Divide 72 in the ratio 4 : 5

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Answer

To divide 72 in the ratio of 4 : 5, we first find the total parts in the ratio.

This can be calculated as:

$4 + 5 = 9$

Next, we calculate the value of one part by dividing the total amount by the total parts:

$\text{Value of one part} = \frac{72}{9} = 8$

Now we can find the amounts for each part of the ratio:

For the first part (4): $4 \times 8 = 32$
For the second part (5): $5 \times 8 = 40$

Thus, 72 divided in the ratio of 4 : 5 gives us 32 and 40.

Step 2

Work out the number of books borrowed by Clara

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Answer

In the ratio of books borrowed by Clara and Dave, Clara : Dave is 3 : 7. Since Dave borrowed 35 books, we can set up a proportion to find the number of books borrowed by Clara:

Let the number of books borrowed by Clara be represented as $C$ . Then we can express the ratio as:

$\frac{C}{35} = \frac{3}{7}$

Cross-multiplying gives us:

$7C = 3 \times 35$

Now, calculate the right side:

$3 \times 35 = 105$

Thus, we have:

$7C = 105$

To find $C$ , divide both sides by 7:

$C = \frac{105}{7} = 15$

Therefore, Clara borrowed 15 books.

7 (a) Divide 72 in the ratio 4 : 5 - OCR - GCSE Maths - Question 7 - 2020 - Paper 1

Worked Solution & Example Answer:7 (a) Divide 72 in the ratio 4 : 5 - OCR - GCSE Maths - Question 7 - 2020 - Paper 1

Divide 72 in the ratio 4 : 5

Work out the number of books borrowed by Clara

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