Question

A medal for whoever helped me with this!

In order to increse his sales, a shopkeeper mixes two types of hard candy: peppermints and cinnamon candies. The peppermints sell for $1.80/kg. The cinnamon candy sells for $2.40/kg. The new candy mixture sells for $2.16/kg. The shopkeeper makes up 50 kg of the new mixture. Use a graph to determine the amount of each type of candy that is needed to make the new mixture. Verify your answer.

Answer 1

Ok, Here let us keep the amount of Peppermint as P and amount of Cinnamon as C

we know P + C = 50 (given) ----> Equation (1)

1.8 P + 2.4 C will be the Cost of this mixture.

But the price is already set at 2.16/kg

so the sale of 50 Kg will fetch him a revenue of 50 x 2.16 = $108

But this sale should give him a profit. So his cost should be less than $108

So if I write the inequality I get

1.8 P + 2.4 C < 108 ----- Inequality (1)
From Equation 1 I have C = 50 - P

If I substitute that in the inequality I get

1.8 P + 2.4 (50-P) < 108

1.8 P + 120 - 2.4 P < 108

-0.6P + 120 < 108

120 - 108 < .6 P

12 < .6P

12/.6 < P

20 < P or P > 20

This means I have to have an amount of P that is more than 20Kg for me to turn a profit.

So my C should be less than 20

20 < P < 50 and 0 < C <20

Answer 2

Let me see how to do it in a graph

Answer 3

sorry C < 30

Answer 4

They break even when P = 20 and C = 30. To make a profit P > 20 and C < 30