Question

(I just need help setting this up please!) 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

want to do it with numbers?

Answer 2

ok lets do it with numbers...

Answer 3

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

Answer 4

idk

Answer 5

hint, the total is 70 pounds, you used 20

Answer 6

oh ok 50

Answer 7

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

Answer 8

um \(3.90\times 20\)?

Answer 9

yea right aka \(\$78\)

Answer 10

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

Answer 11

yeah, \(2.50\times 50=125\) so what would the total be?

Answer 12

add right? 78+125=203

Answer 13

yes, and 203 at 70 pounds would be what ?

Answer 14

203/70=2.9?

Answer 15

so what do we do now?

Answer 16

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 17

??

Answer 18

how did you get the 50?

Answer 19

oh subtract \(70-x\) right?

Answer 20

yes subtract
now the \(x\) pounds of \(\$3.90\) candy cost \(3.90\times x\) how much does the other candy cost?

Answer 21

must be \(2.50\times (70-x)\) ?

Answer 22

right, and the total has to be \(70\times 3.30\) so set \[3.9x+2.5\times (70-x)=70\times 3.3\] and solve for \(x\)

Answer 23

ooh ok

Answer 24

i get it
thanks !

Answer 25

cant you do this some other way?

Answer 26

sure, the math teacher way
say \[x+y=70\\
3.9x+2.5y=3.3\times 70\] but all the work is teh same

Answer 27

@satellite73 you are outstanding!!! :)