Algebra-Context Inequality Systems Graphically

Question

Ava and her children went into a movie theater where they sell drinks for $5.50 each and candies for $3 each. Ava has $45 to spend and must buy at least 10 drinks and candies altogether. If x represents the number of drinks purchased and y represents the number of candies purchased, write and solve a system of inequalities graphically and determine one possible solution.

I need 2 Inequalities that start with y

Answer 1

Hello, Chad,

Use x for the number of drinks and y for the number of candies.

We know the sum of x and y must be at least 10.

x + y => 10

x =>(10 - y)

Or, if you'd like, rearrange to find y to get one of your "two inequalities that start with y.": [I'm not sure why this is stipulated].

y =>(10 - x)

We also know that we can get the total amount spent by summing the cost of drinks, 5.5*x and the cost of candies, 3*y. Set that equal to the $45 Ava plans to spend:

5.5*x + 3*y = 45

Now use the first equation for y:

5.5x + 3*(10-y) = 45

5.5x + 30 - 3x = 45

2.5x + 30 = 45

2.5x = 15

x = 6

Then y = 4

3y = 45 - 5.5(10-x)

3y = 45 -55 + 5.5x

y = 15-(5.5/3)*x

Now use the first equation in this one to find y:

y = 15 - (5.5/3)*(10-y)

y = 15 - (55/3) + (5.5/3)y

y - (5.5/3)y = 15 -55/3

Check to see if this works:

Candies (y) 4 at $3 each - $12

Drinks (x) 6 at $5.50 each = 33

Total = $45

It works.

Bob