Pastaroni is a local Italian restaurant that serves a specialized pasta salad. Included in this salad is macaroni, linguine and bow-tie pasta. The salad contains six times as much linguine as it does macaroni. Both macaroni and linguine sell for $4; bow-tie pasta sells for $8. If the restaurant makes 140 pounds of pasta every day, how many pounds of each type of pasta are needed if the salad sells for $6?

Question

anonymous · Answer

Let M, L and BT be the pound weight of macaroni, linfuine and bow-tie pasta respectively.

Solve the following equations for M, L and BT:$$\left\{L+M+\text{BT}=140,\frac{4L+4M+8\text{BT}}{140}=6,\frac{L}{M}=6\right\}$$$$\{L=60,M=10,\text{BT}=70\} $$Verify the result:$$\frac{60*\text{$\$$4}+10*\text{$\$$4}+70*\text{$\$$8}}{140}=\text{$\$$6} $$

anonymous · Answer

Sorry, linfuine should have been written, linguine.

anonymous · Answer

THANKS!!

anonymous · Answer

You are welcome and thank you for the medal.

anonymous · Answer

Okay wait, how did you get L=60 M=10 and b=70

anonymous · Answer

@CamW

Refer to the attached Mathematica calculation to see how the values of L, M and BT were determined.