Find the cost per pound of the peanuts and M&M's.

Question

A storeowner mixed 8 pounds of peanuts and 5 pounds of M&M's. This 13 pound mixture sold for $55.27. A second mixture included 6 pounds of peanuts and 4 pounds of M&M's. This 10 pound mixture sold for $42.70. 

Answer 1

Cost of peanut = $x / pound

cost of M & M =$y /pound
A storeowner mixed 8 pounds of peanuts and 5 pounds of M&M's

This 13 pound mixture sold for $55.27

8x+5y=55.27 ______________ equation 1



A second mixture included 6 pounds of peanuts and 4 pounds of M&M's.

This 10 pound mixture sold for $42.70

6x+4y= 42.70 _______________equation 2

 

 

multiply equation 1 with -4 and equation 2 with 5 and add them

 

-32x-20y=-221.08

30x+20y=213.5

________________

 

-2x =-7.58

 

x=3.79

 

substitute x=3.79 in equation 1

 

8x+5y=55.27

 

 

8(3.79)+5y=55.27

30.32 +5y=55.27

5y=24.95

y=4.99

 

Cost of peanut = $x / pound=$3.79/pound

cost of M & M =$y /pound=$4.99/pound