#23 on my homework...need help!!?

Question

A dealer has some hard candy worth $2.00 a pound and some worth $3.00 a pound. He wishes to make a mixture of 80 pounds that he can sell for $2.20 a pound. How many pounds of each kind should he use?

Answer 1

Let the amount of the candy costing $2.00 a pound be 'x' pounds and the amount of candy costing $3.00 a lb. be 'y' lb. in the mixture weighing 80 lb.

therefore,
x + y = 80
or, y = 80 - x.............(i)

cost of the first type of candy in the mixture = $2x
cost of the second type of candy in the mixture = $3.00y

By condition,

2x + 3y = 80*2.20

But from (i),

2x + 3(80 - x) = 176
or, 2x + 240 - 3x = 176
or, -x = 176-240
or, -x = -64
or, x = 64

Also,
y = 80 - x
or. y = 80 - 64
or, y = 16

Ans.:
Wt. of first type of candy = 64 pounds
Wt. of second type of candy = 16 pounds

Answer 2

Since we don’t know how much of each type to use, let’s call x the amount of $2per pound candy. So, we have the following picture setup

x + 80 lbs -x=80x2.20

2x+3(80-x)=80x2.20

2x + 240 -3x =176

240-x = 176

-x = -64

x=64

go back plug in the first equation

64+80-64=80
80=80

64 lbs of 2.00 candy
16 lbs of 3.00 candy
=80 lbs of 2.20 candy

good luck

Answer 3

equation and work:::

2x+3(80-x)=176
1) remove parenthesis using distributive property
2x+240-3x=176
2) combine like terms, if there are any
2x-3x+240=176
-1x+240=176
3) subtract 240 from both sides to isolate the variable
-1x+240-240=176-240
4) the plus 240 and the minus 240 cancel each other out leaving..
-1x=176-240
5) subtract 176-240
-1x=-64
6) divide both sides by -1
x=64

so that is type a (the 2.00/lb).
then your going to do 80-x to find the how much of type b (the 3.00/lb). 80-64=x.
x=16

so you should get 64lbs of the first type and 16 of the second type.

Answer 4

h pounds of $2 hard candy
+ c pounds of $3 hard candy
= 80 pounds of $2.20 mixed candy
2h + 3c = 80*2.20
2h + 3c = $176

then you can do one of two things
1) guess & check
2) algebra with substitution

64 pounds of $2 candy
+ 16 pounds of $3 candy
= 80 pounds of $2.20 candy

Answer 5

I also answered your previous question...same set up
x+y=80
y= 80-x

2.00x + 3.00 (80-x) = here you'll need to figure the total amount he'll make from his 80lbs of candy at $2.20/lb

2.00x + 3.00 (80-x) = 80($2.20)