Question

Mandy's Candies is most famous for their homemade fudge and homemade toffee. They make an average of 146 pounds of fudge and toffee combined each month. They sell a pound of fudge for $8.29 and a pound of toffee for $6.26. Mandy's averages $1,045.91 each month in fudge and toffee sales. On average, how many pounds each of fudge and toffee does Mandy's Candies sell in one month?






65 fudge; 81 toffee





54 fudge; 92 toffee





71 fudge; 75 toffee





68 fudge; 78 toffee

Answer 1

Looks like you need to set up a couple equations , and solve the system here

Answer 2

Lets define the variables first

Answer 3

Let F= Fudge
T = Toffee

Answer 4

Total Pounds = #Fudge + #toffee
total money = (price toffee)(#Toffee) + (Price fudge)(#fudge)

Answer 5

see the logic in those 2 statements

Answer 6

Using the variables that we defined T and F, putting those 2 statements into equations gives

146 = T + F (Pounds)

1045.91 = 6.26*T + 8.29*F (Money)

Answer 7

u understand that , or need more explanation

Answer 8

A little more please bcuz I suck at math im only good at basics

Answer 9

do you see how i arrived at those 2 equations?

Answer 10

yes

Answer 11

They make an average of 146 pounds of fudge and toffee combined each month

Total = pounds toffee + pounds fudge

146 = T + F

Answer 12

They sell a pound of fudge for $8.29 and a pound of toffee for $6.26. Mandy's averages $1,045.91 each month in fudge and toffee sales.

Total Sales = Price fudge x #pounds fudge sold + Price Toffee x # pounds toffee sold

1045.91 = 8.29*F + 6.26*T

Answer 13

The two equations are:

146 = T + F
1045.91 = 8.29*F + 6.26*T

Answer 14

good so far?

Answer 15

yes

Answer 16

ok, to solve these and figure out which T and F values will satisfy both equations, we can do a substitution...

Answer 17

By that i mean, Solve the first equation for either T= or F=, and then substitute that value into the second equation, so you have only one variable in the equation.

Answer 18

146 = T + F
1045.91 = 8.29*F + 6.26*T

Solving first for T: T = 146 - F
Substitute that T value into the second equation:

1045.91 = 8.29*F + 6.26*(146 - F)

Answer 19

good on that part?

Answer 20

yes

Answer 21

cool, now you have an equation with only one variable, F, we can solve that for F=

1045.91 = 8.29*F + 6.26*(146 - F)

Answer 22

First thing , distribute the 6.26 into the parenthesis by multiplying each by 6.26...

1045.91 = 8.29*F + 6.26*(146 - F)

1045.91 = 8.29*F + 913.96 - 6.26*F

Answer 23

Now, we can combine the like terms

1045.91 = 8.29*F + 913.96 - 6.26*F

1045.91 = (8.29-6.26)*F + 913.96

1045.91 = 2.03*F + 913.96

Answer 24

Subtract 913.96 from both sides

1045.91 - 913.96 = 2.03*F + 913.96 - 913.96

131.95 = 2.03*F

Answer 25

Divide both sides by 2.03

131.95 / 2.03 = (2.03/2.03) F

65 = F

Answer 26

There you have it,

F = 65 , 65 pounds of Fudge was sold

Answer 27

good on that part?

Answer 28

yes thank you for explaining it

Answer 29

welcome,

That is all you need to do on this one, the only answer with F=65 is the first one.

If you needed the pounds of toffee too, it is just one more simple step

You have F=65 , put that into the first equation

T+ F = 146

T + 65 = 146

T = 146 - 65
T = 81 pounds toffee