The drama club sells hot drinks during intermission for the school play. At one performance they sold $200 worth of drinks. Karen knows that they sold 295 total drinks. If hot chocolate sold for $0.75 and coffee sold for $0.50, then how many of each hot drink did the drama club sell?

they sold 210 hot chocolates and 85 coffees

Step-by-step explanation:

We know that they sold $200 worth of drinks

x will be the number of hot chocolates sold

y will be the number of coffees sold

This means that

.75x+.5y=200

We also know that they sold 295 total drinks which means that

x+y=295

This is a system of linear equations which I will solve through substitution

x+y=295

Subtract y from both sides and divide by -1 to get

-x+295=y

Plug y into the first equation and get

.75x+.5(-x+295)=200

Distribute the .5 and simplify to get

.75x-.5x+147.5

.25x+147.5=200

Subtract 147.5 and then divide by .25 to get our x value

x=210

Now we can go back and plug this in into our equation

210+y=295

Subtract 210 to get y

y=85

This means that they sold 210 hot chocolates and 85 coffees

27 + 13x + 15 = (x + 5)( =

step-by-step explanation:

27 + 13x + 15 = (x + 5)( = 27 + 13x + 15 = (x + 5)( = 27 + 13x + 15 = (x + 5)( =

the revenue of the fitness center, y, is the product of two factors: the number of members and the fee paid by each member. there are 320 members now, but number of members goes down by 10 for each $5 increase in fees, so if x is the number of $5 price increases then members is equal to (320 - 10x). since the fee is currently $45, and the fee increases by $5 for every price bump x, the fee is given by (45 + 5x). so, revenue y is given by y = (320 - 10x)(45 + 5x).