Chase works at a frozen yogurt store during the summer. He needs to order 5 oz and 8 oz cups. To get free shipping, he must order at least 10 boxes of cups. A box of 5 oz cups cost $100 and a box of 8 oz cups cost $150. A maximum of $1200 is budgeted for cups. Use x and y as your variables.

Question

Chase works at a frozen yogurt store during the summer. He needs to order 5 oz and 8 oz cups. To get free shipping, he must order at least 10 boxes of cups. A box of 5 oz cups cost $100 and a box of 8 oz cups cost $150. A maximum of $1200 is budgeted for cups. Use x and y as your variables.

Answer 1

Write the equation that represents the number of boxes of cups.

Write the equation that represents the number of each cup.

How do I write this?

Answer 2

X boxes of 5 oz. cups

Y boxes of 8 oz. cups.

Eq1: x + y = 10.
Eq2: 100x + 150y = 1200.
Multiply Eq1 by -100 and add the Eqs:
-100x -100y = -1000
100x + 150y = 1200
sum: 50y = 200
Y = 4.

In Eq1, rreplace Y with 4 and solve for X.

Answer 3

Let x represent the number of boxes of 5 oz cups Chase orders, and y represent the number of boxes of 8 oz cups he orders.

We know that Chase needs to order at least 10 boxes of cups to get free shipping. So, the constraint for the number of boxes is:

x + y ≥ 10

We also know that a box of 5 oz cups costs $100 and a box of 8 oz cups costs $150. The constraint for the budget is:

100x + 150y ≤ 1200

Now, let's solve this system of inequalities to find the feasible options for Chase.

To graph these constraints, we'll plot the lines x + y = 10 and 100x + 150y = 1200 on a Cartesian coordinate system.

To find the x-intercept of x + y = 10, we set y to 0 and solve for x:

x + 0 = 10
x = 10

To find the y-intercept, we set x to 0 and solve for y:

0 + y = 10
y = 10

So, our first point is (10, 0). Moving 10 units to the right and 10 units up from this point, we find another point (20, 10).

To find the x-intercept of 100x + 150y = 1200, we set y to 0 and solve for x:

100x + 150(0) = 1200
100x = 1200
x = 12

To find the y-intercept, we set x to 0 and solve for y:

100(0) + 150y = 1200
150y = 1200
y = 8

So, our second point is (0, 8). Moving 12 units to the right and 8 units up from this point, we find another point (12, 16).

Now, let's draw these two lines on the graph and shade the feasible region.

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0 10 12

The feasible region is the shaded area in the graph. The feasible options for x and y, within the given constraints, are the points within that region.

To find the specific feasible points, we can substitute the values of x and y into the equation x + y = 10.

Let's calculate a few options:

For (10, 0): 10 + 0 = 10 (satisfies the equation)
For (20, 10): 20 + 10 = 30 (does not satisfy the equation)

Therefore, the feasible options for x and y within the given constraints are (10, 0) and any other combinations within the shaded region that satisfy x + y = 10.

These feasible options represent the number of boxes of 5 oz cups (x) and 8 oz cups (y) that Chase can order to stay within his budget, get free shipping, and meet the required number of boxes.