Dee wants to mix coffee worth $7 pound with coffee worth $4 a pound to get a mixture of 14 pounds $5 a pound . How many pounds o
f each must be mixed together to get the new blend?
1 answer:
![\bf \begin{array}{lccclll} &amount&price&cost\\ &-----&-----&-----\\ \textit{\$7/lb coffee}&x&7&7x\\ \textit{\$4/lb coffee}&y&4&4y\\ -----&-----&-----&-----\\ blend&14&5&14\cdot 5 \end{array}](https://tex.z-dn.net/?f=%5Cbf%20%5Cbegin%7Barray%7D%7Blccclll%7D%0A%26amount%26price%26cost%5C%5C%0A%26-----%26-----%26-----%5C%5C%0A%5Ctextit%7B%5C%247%2Flb%20coffee%7D%26x%267%267x%5C%5C%0A%5Ctextit%7B%5C%244%2Flb%20coffee%7D%26y%264%264y%5C%5C%0A-----%26-----%26-----%26-----%5C%5C%0Ablend%2614%265%2614%5Ccdot%205%0A%5Cend%7Barray%7D)
so.. whatever "x" and "y" amounts are, we know that, added together, they must yield 14lbs
thus x + y = 14
and whatever the cost of each is, 7x + 4y must be 14*5
7x+4y = 70
thus
![\bf \begin{cases} x+y=14\to \boxed{y}=14-x\\\\ 7x+4y=70\\ ----------\\ 7x+4\left( \boxed{14-x}\right)=70 \end{cases}](https://tex.z-dn.net/?f=%5Cbf%20%5Cbegin%7Bcases%7D%0Ax%2By%3D14%5Cto%20%5Cboxed%7By%7D%3D14-x%5C%5C%5C%5C%0A7x%2B4y%3D70%5C%5C%0A----------%5C%5C%0A7x%2B4%5Cleft%28%20%20%5Cboxed%7B14-x%7D%5Cright%29%3D70%0A%5Cend%7Bcases%7D)
solve for "x", to see how much of the $7/lb type will be needed
what about the $4/lb one? well, y = 14 - x
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