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AQA GCSE · Question 19 · Ratio Proportion and Rates of Change
A, B and C are numbers.
Here is some information about B and C.
B = 7/4 of A
C = A increased by 150%
Work out C as a fraction of B.
<br/><br/>
<table border="1" cellpadding="20" cellspacing="0" style="border-collapse: collapse; font-family: Times New Roman, serif; font-size: 24px;">
<tr>
<td style="font-style: italic; width: 80px; text-align: center;"><i>B</i></td>
<td style="padding: 20px 40px;"><sup>7</sup>/<sub>4</sub> of <i>A</i></td>
</tr>
<tr>
<td style="font-style: italic; text-align: center;"><i>C</i></td>
<td style="padding: 20px 40px;"><i>A</i> <b>increased by 150%</b></td>
</tr>
</table>
A, B and C are numbers.
Here is some information about B and C.
B = 7/4 of A
C = A increased by 150%
Work out C as a fraction of B.
<br/><br/>
<table border="1" cellpadding="20" cellspacing="0" style="border-collapse: collapse; font-family: Times New Roman, serif; font-size: 24px;"> <tr> <td style="font-style: italic; width: 80px; text-align: center;"><i>B</i></td> <td style="padding: 20px 40px;"><sup>7</sup>/<sub>4</sub> of <i>A</i></td> </tr> <tr> <td style="font-style: italic; text-align: center;"><i>C</i></td> <td style="padding: 20px 40px;"><i>A</i> <b>increased by 150%</b></td> </tr> </table>How to approach this question
1. Write algebraic expressions for B and C in terms of A.
- For B, this is straightforward: B = (7/4)A.
- For C, "increased by 150%" means you have the original 100% plus an extra 150%, which is 250% of A in total. Convert 250% to a fraction.
2. The question asks for "C as a fraction of B", which means you need to calculate the value of C/B.
3. Substitute your expressions for C and B into the fraction C/B.
4. The variable A should cancel out.
5. Simplify the resulting fraction of fractions.
Full Answer
Step 1: Express B and C in terms of A.
B = (7/4)A
To increase A by 150%, we find 150% of A and add it to A.
150% of A = 1.5 * A = (3/2)A
C = A + (3/2)A = (2/2)A + (3/2)A = (5/2)A
Step 2: Work out C as a fraction of B. This means we need to calculate C/B.
C/B = [(5/2)A] / [(7/4)A]
Step 3: The A's cancel out.
C/B = (5/2) / (7/4)
Step 4: To divide by a fraction, we multiply by its reciprocal.
C/B = (5/2) * (4/7)
C/B = (5 * 4) / (2 * 7) = 20 / 14
Step 5: Simplify the fraction.
20 / 14 = 10 / 7
Answer: 10/7
We are given relationships between A, B, and C. We need to find the value of the fraction C/B.
1. **Express B in terms of A:**
B = 7/4 of A
B = (7/4)A
2. **Express C in terms of A:**
C = A increased by 150%
This means C is the original amount (100% of A) plus the increase (150% of A).
C = 100% A + 150% A = 250% A
To convert the percentage to a fraction: 250% = 250/100 = 25/10 = 5/2.
So, C = (5/2)A
3. **Calculate C as a fraction of B (C/B):**
C/B = ( (5/2)A ) / ( (7/4)A )
The `A` on the top and bottom cancels out:
C/B = (5/2) / (7/4)
4. **Divide the fractions:** To divide by a fraction, you multiply by its reciprocal (flip it upside down):
C/B = 5/2 × 4/7
C/B = (5 × 4) / (2 × 7) = 20/14
5. **Simplify:**
C/B = 20/14 = 10/7
The final answer is 10/7.
Common mistakes
✗ Incorrectly calculating the percentage increase. A common mistake is to find 150% of A and call that C, instead of adding it to A. (C = 1.5A instead of C = 2.5A).
✗ Errors in dividing fractions.
✗ Calculating B/C instead of C/B.
✗ Leaving the answer unsimplified (20/14).
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