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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.​

Sagot :

mhanifa

Answer:

  • a = 80,
  • b = 84,
  • c = 60

=======================

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
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