There are 450 coupons which can be used in Pedicure and Hair cutting. Ratio between
Males to Females who use their coupons in Hair cutting is 13 : 7 Number of males who use their coupons
in Pedicure is 72 more than number of females who use their coupon in Hair cutting. Total number of males
who use their coupon in Pedicure and Haircutting together is 174 more than total number of females who
use their coupon in Pedicure and Haircutting together.

Ratio between Males who use their coupon in Pedicure to that of in Spa is $4 : 5$, while ratio between Females who use their coupon in Haircutting to that of in Spa is $6 : 11$. Find the total number of people who use their coupons in Spa.

Question

There are 450 coupons which can be used in Pedicure and Hair cutting. Ratio between
Males to Females who use their coupons in Hair cutting is 13 : 7 Number of males who use their coupons
in Pedicure is 72 more than number of females who use their coupon in Hair cutting. Total number of males
who use their coupon in Pedicure and Haircutting together is 174 more than total number of females who
use their coupon in Pedicure and Haircutting together.

Ratio between Males who use their coupon in Pedicure to that of in Spa is $4 : 5$, while ratio between Females who use their coupon in Haircutting to that of in Spa is $6 : 11$. Find the total number of people who use their coupons in Spa.

Accepted Answer

**Solution:**

1. Let the number of males who use coupons in Spa be $x$.
2. Given the ratio of males using coupons in Pedicure to Spa is $4 : 5$, so if males in Pedicure are $4k$, then males in Spa are $5k$. Here, $x = 5k$.
3. Similarly, let the number of females who use coupons in Spa be $y$.
4. The ratio of females using coupons in Haircutting to Spa is $6 : 11$, so if females in Haircutting are $6m$, then females in Spa are $11m$. Here, $y = 11m$.
5. From the problem, males in Spa = $195$ and females in Spa = $154$ (given or calculated from the ratios).
6. Total number of people who use coupons in Spa = males in Spa + females in Spa = $195 + 154 = 349$.

**Answer:** $349$

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