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Solved on Oct 30, 2023

A club has a membership ratio of men to women 1:4 and full to off-peak 3:2. It has 120 members and aims to increase by 20%20 \%. (i) How many more women would you expect to add? (ii) How many of the new members are likely to sign up for off-peak?

STEP 1

Assumptions1. The ratio of men to women is14. The ratio of full members to off-peak members is33. The current total membership is1204. The club aims to increase its membership by20%
5. The ratios will remain the same after the increase

STEP 2

First, we need to find the total number of members the club aims to have after the increase. We can do this by multiplying the current total membership by1 plus the percentage increase.
New total membership=Current total membershiptimes(1+Percentage increase)New\, total\, membership = Current\, total\, membership \\times (1 + Percentage\, increase)

STEP 3

Now, plug in the given values for the current total membership and percentage increase to calculate the new total membership.
New total membership=120times(1+20%)New\, total\, membership =120 \\times (1 +20\%)

STEP 4

Convert the percentage to a decimal value.
20%=0.220\% =0.2New total membership=120times(1+0.2)New\, total\, membership =120 \\times (1 +0.2)

STEP 5

Calculate the new total membership.
New total membership=120times1.2=144New\, total\, membership =120 \\times1.2 =144

STEP 6

Now that we have the new total membership, we can find the number of new members the club aims to add. This is the difference between the new total membership and the current total membership.
New members=New total membership−Current total membershipNew\, members = New\, total\, membership - Current\, total\, membership

STEP 7

Plug in the values for the new total membership and the current total membership to calculate the number of new members.
New members=144−120New\, members =144 -120

STEP 8

Calculate the number of new members.
New members=144−120=24New\, members =144 -120 =24

STEP 9

(i) To find the number of new women members, we multiply the number of new members by the ratio of women to the total ratio of men and women.
New women members=New memberstimesWomen ratioTotal ratioNew\, women\, members = New\, members \\times \frac{Women\, ratio}{Total\, ratio}

STEP 10

Plug in the values for the new members and the ratios to calculate the number of new women members.
New women members=24times45New\, women\, members =24 \\times \frac{4}{5}

STEP 11

Calculate the number of new women members.
New women members=24times45=19.New\, women\, members =24 \\times \frac{4}{5} =19.Approximately19 more women would you expect to add to the membership.

STEP 12

(ii) To find the number of new off-peak members, we multiply the number of new members by the ratio of off-peak members to the total ratio of full and off-peak members.
New off−peak members=New memberstimesOff−peak ratioTotal ratioNew\, off-peak\, members = New\, members \\times \frac{Off-peak\, ratio}{Total\, ratio}

STEP 13

Plug in the values for the new members and the ratios to calculate the number of new off-peak members.
New off−peak members=24times25New\, off-peak\, members =24 \\times \frac{2}{5}

STEP 14

Calculate the number of new off-peak members.
New off−peak members=24times2=9.6New\, off-peak\, members =24 \\times \frac{2}{} =9.6Approximately10 of the new members are likely to sign up for off-peak membership.

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