algebra word problem

Question

Keil is going to make 13 pounds of mixed nuts for a party. Peanuts cost $3.00 a pound and fancy nuts cost $6.00 per pound. If Keil can spend $63.00 on nuts, how many pounds of each should he buy?

Answer 1

I love these problems! One method is to set up a system of equations. Let's make the number of pounds of peanuts p and pounds of fancy nuts f

Cost of peanuts=3p

Cost of fancy=6f

Total cost = 63 = 3p+6f

Total weight = 13 = p+f

 

I'd like to try elimination by multiplication. I'm going to multiply our second equation by 3

 

63=3p+6f

39=3p+3f

 

Now I'm going to subtract the second equation from the first

 

24=0p+3f

24=3f

8=f

 

Now substitute that back in to get the other answer.

 

13=p+f

13=p+(8)

5=p

 

Five pounds of peanuts and eight pounds of fancy nuts! we can also check that this answer makes sense with our other equation

 

3p+6f

3(5)+6(8)

15+48

63