If you have red candy that is $1.96 a pound and lemon candy that is $2.16 per pound, find the amount of each candy needed to make 5 pounds of candy that is $2 a pound.

Answer 1

This is a mixture and a system of equations problem. First, we are going to identify the variables for the candy. I will use r for the red candy and L for the lemon candy.

We first set up the equation for the pounds of candy. r +L = 5 This shows us that the pounds of each candy need to be combined (or summed) to make 5 pounds.

Next, we set up the second equation, which will allow us to find the amounts and their costs. The (5) on the right side of the = signifies that there will be 5 pounds total.

1.96r + 2.16L = 2(5)

If decimals are scary, then it can be rewritten as 196r + 216L = 200(5)

Now we solve the first equation for either r or L. Let' solve for L. This gives L=5-r

Next, we substitute that equation into the second equation in place of L.

196r +216(5-r) = 1000

Next, let's distribute the 216. 196r+ 1080 - 216r = 1000.

After that, we combine the like terms and subtract 1080 from 1000.

-20r = -80.

Yes, we have negative values, but this is ok since there are negatives on both sides. They will cancel each other out. We divide 80 by 20 to get r = 4. This means that we will need 4 pounds of the red candy.

5-r = L L=5-4 =1, L=1

We will need 1 pound of the lemon candy to match with the red candy to get 5 pounds of the mixture which will cost $2 a pound.

Answer 2

In this problem, we need to solve for 2 unknowns: the amount of red (r) and the amount of lemon (L) in pounds

For 2 unknowns, we need 2 equations, so we'll come up with

1. an equation based on total weight, and
2. an equation based on total cost

We want a total weight of 5 pounds, so that's our first equation

r + L = 5

The total cost is the amount we'll spend on red + the amount we'll spend on lemon

1. Red costs $1.96 a pound, so r pounds of red costs 1.96r
2. Lemon costs $2.16 a pound, so L pounds of lemon costs 2.16L
3. We want the mix to cost $2 a pound, and we want 5 pounds, so the total cost is $2 × 5 = $10

Our second equation, then, is

1.96r + 2.16L = 10

Now, we just solve for r and L

I like the substitution method here

Solve for r in the first equation

r = 5 - L

Substitute 5 - L for r in the second equation

1.96(5 - L) + 2.16L = 10

Solve for L

9.8 - 1.96L + 2.16L = 10

0.2L = 0.2

L = 1

Substitute 1 for L in the first equation

r = 5 - 1 = 4

The answer's 4 pounds of red and 1 pound of lemon

Answer 3

1.96x + 2.16y = 2(x+y)= 2(5) = 10

1.96(5-y) + 2.16y = 10

2.16y - 1.96y = 10 - 5(1.96) =10- 9.80

.2y = .2

y = 1 pound of $2.16 lemon

x = 4 pounds of $1.96 red candy

to get 5 pounds of $2 mixture

another (less conventional) method:

2-1.96 = .04

2.16-2 = .16

.16/.04 = 4 times as much red as lemon

x/y = 4

x/(5-x) = 4

20-4x= x

5x=20

x = 4 pounds red

y=5-x= 5-4 = 1 pound lemon