Question

A confectioner is going to mix candy worth $3.90 per pound with candy worth $2.50 per pound to obtain 70 pounds of candy worth $3.30 per pound. How many pounds of each kind should she use?

Answer 1

say you use 20 pounds of the $3.90 candy.
how many pounds of the $2.50 would you use?

Answer 2

idk

Answer 3

hint, the total is 70 pounds, you used 20

Answer 4

oh ok 50

Answer 5

right , and what would the cost of the $3.90 candy be total?

Answer 6

um 3.90 x 20 ?

Answer 7

yeah right aka $78

Answer 8

oh ok and the 50 pounds at $2.50 would cost $125 right?

Answer 9

yeah, 2.50×50=125 so what would the total be?

Answer 10

add right? 78+125=203

Answer 11

yes, and 203 at 70 pounds would be what ?

Answer 12

203/70=2.9?

Answer 13

so what do we do now?

Answer 14

try again, this time with variables
say you use x amount of $3.90 candy, how much of the $3.90 candy do you use?

Answer 15

??

Answer 16

how did you get the 50?

Answer 17

oh subtract 70−x right?

Answer 18

yes subtract
now the x pounds of $3.90 candy cost 3.90×x how much does the other candy cost?

Answer 19

must be 2.50×(70−x) ?

Answer 20

right, and the total has to be 70×3.30 so set
3.9x+2.5×(70−x)=70×3.3
and solve for x

Answer 21

ooh ok

Answer 22

I get it, thanks!