Question

Amy thinks of three numbers, which she calls a, b and c. The ratio a: cis 4: 3. The ratio b: cis 7:5. The median of a, b and c is 80. Work out the values of a, b and c.​

Answer 1

• a = 80,
• b = 84,
• c = 60

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Given

• a : c = 4 : 3
• b : c = 7 : 5
• The median is 80.

From the ratios we see both a and b are greater than c.

Let's find the smaller of the two, which is the median when the numbers are ordered.

• a = (4/3) c
• b = (7/5) c

Compare the fractions:

• 4/3 vs 7/5
• (4*5)/(3*5) vs (7*3)/(5*3)
• 20/15 vs 21/15
• 20 < 21, so
• 4/3 < 7/5, so a < b

or

• c < a < b

As per above, the median is a, which is 80.

Find the value of c:

• (4/3)c = 80
• c = 80*3/4
• c = 60

Find b:

• b = (7/5)*60
• b = 84