Question

Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.

The drama club is selling gift baskets to raise money for new costumes. During the fall play, they sold a combined 11 regular gift baskets and 11 deluxe gift baskets, earning a total of $671. During the spring musical, they sold 27 regular gift baskets and 8 deluxe gift baskets, earning a total of $830. How much are they charging for the different sized gift baskets?

The drama club is charging $?
for a regular gift basket and $? for a deluxe gift basket.

bro help me im gonna dieeeee omlllll

Answer 1

Regular gift baskets = $18, Deluxe gift baskets = $43

Explanation:

First, let's identify which basket is each for our equation:

Regular Gift Baskets = x

Deluxe Gift Baskets = y

The problem gives us two events in which they tell how many baskets are sold and how much they make in total after the event. We can create two equations:

11x + 11y = 671

27x + 8y = 830

We now have two unknowns and two equations. What we can do here is get one equation equal to an unknown variable and plug that variable into the other equation where we can create an equation with just one unknown to solve for

Let's get y by itself by doing some algebra using the equation below:

27x + 8y = 830

8y = 830 - 27x

y = (830 - 27x) / 8

Now, we can plug this variable into the other equation:

11x + 11y = 671

11x + 11((830 - 27x) / 8) = 671

Now, solve for x:

11x + 11((830 - 27x) / 8) = 671

11x + (9130 - 297x)/8 = 671

(9130 - 297x)/8 = 671 - 11x

9130 - 297x = 5368 - 88x

9130 - 297x + 88x = 5368

9130 - 209x = 5368

-209x = -3762

209x = 3762

x = 18

Now, that we have the x variable, we can plug it into our y equation to solve for y:

y = (830 - 27(18))/8

y = 43

Thus, the Normal Gift Basket will cost $18 and the Deluxe Gift Basket will cost $43

You can always check your work by plugging the values you solve for into the original equation to see if the output matches. For example:

11(18) + 11(43) = 671

Hope this helps :)