Question

Rachel has 30 pounds of a mixture of candy that sells for $1.00/lb. If lollipops sell for $0.95/lb and caramel candies sell for $1.10/lb. How many pounds of lollipops are in the mixture?

Answer 1

20 pounds of lollipops. 20 x .95 = 19, 10 x 1.1 = 11. sorry i'm awful at explaining math.

Answer 2

Answer:

20 pounds

Step-by-step explanation:

Let x represent the number of pounds of lollipops and y represent the number of pounds of caramel candies.  The first equation is

x + y = 30,

since the combined numbers of pounds of lollipops and caramel candies.

The lollipops sell for 0.95/lb; this gives us the expression 0.95x.

Caramel candies sell for 1.10/lb; this gives us the expression 1.10y.

Together they make a 30 pound mixture that sells for 1.00/lb; this gives us the expression 30(1.00), which simplifies to 30.

This together gives us the equation

0.95x+1.10y = 30

This gives us the system

$\left \{ {{x+y=30} \atop {0.95x+1.10y=30}} \right.$

To solve this we will use elimination; we will make the coefficients of x the same by multiplying the top equation by 0.95:

$\left \{ {{0.95(x+y=30)} \atop {0.95x+1.10y=30}} \right. \\\\\left \{ {{0.95x+0.95y=28.5} \atop {0.95x+1.10y=30}} \right.$

Subtract the second equation from the first:

$\left \{ {{0.95x+0.95y=28.5} \atop {-(0.95x+1.10y=30)}} \right. \\\\-0.15y=-1.5$

Divide both sides by -0.15:

-0.15y/-0.15 = -1.5/-0.15

y = 10

There are 10 pounds of caramel candies.

Substitute this into the first equation:

x+10 = 30

Subtract 10 from each side:

x+10-10 = 30-10

x = 20

There are 20 pounds of lollipops.