A lemonade stand sells drinks in two sizes, small and medium. In the span of 1 hour, the stand sold 72 drinks. The ratio of small drinks to medium drinks sold was 5:3. If small drinks cost $0.50 and medium drinks cost $1.00, how much total money did the lemonade stand take in?

The total amount of money received at the lemonade stand was $49.50

Step-by-step explanation:

Let

x ---> the number of small drinks sold

y ---> the number of medium drinks sold

we know that

The stand sold 72 drinks

so

----> equation A

The ratio of small drinks to medium drinks sold was 5:3

----> equation B

substitute equation B in equation A

Find the value of x

Find out the total amount of money received at the lemonade stand

x =±sqrt(1/3)

step-by-step explanation:

x+4/6x=1/x

multiply each side by 6x to get rid of the fractions

6x*(x+4/6x)=1/x*6x

distribute

6x^2 +4 = 6

subtract 4 from each side

6x^2 +4-4 = 6-4

6x^2 =2

divide by 6

6x^2/6 = 2/6

x^2 = 1/3

take the square root of each side

sqrt(x^2) = ±sqrt(1/3)

x =±sqrt(1/3)