Answer:
Peanuts cost $2 a bag
Almonds cost $2.50 a bag
Step-by-step explanation:
To solve, write a system of equations using the information given.
- "a small case contains 10 bags of almonds and 25 bags of peanuts for $75" translates to 10a+25p=75
- "a large case comtains 40 bags of almonds and 60 bags of peanuts for $220" translates to 40a+60p=220
Solve by stacking the equations and performing elimination. To eliminate a variable, the coefficients must be the same. To make this so, we will multiply 10a+25p=75 by 4 to become 40a+100p=300. Now stack the equations and subtract:
40a+100p=300
40a+60p=220
----------------------------
0a + 40p=80
p=2 means peanuts cost $2 a bag.
Substitute p=2 into one equation to find a.
10a+25(2)=75
10a+50=75
10a=25
a=2.5 means almonds cost $2.50 a bag.
