Answer:
C. $4.50
Step-by-step explanation:
hello, there.
1) 2p + 3c = 17.50
2) 5p + 2c = 19.00
:
Solve equation 1 for p
:
p = (17.50 - 3c) / 2
:
Substitute for p in second equation
:
(5(17.50 - 3c) / 2) + 2c = 19.00
:
Multiply both sides of = by 2
:
(5(17.50 - 3c)) + 4c = 38.00
:
87.50 - 15c + 4c = 38.00
:
-11c = -49.50
:
c = 4.50
:
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Cashews are $4.50 per pound
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:have a great day.
Answer:
C
Step-by-step explanation:
Let p represent the cost for one pound of peanuts and let c represent the cost for one pound of cashews.
Two pounds of peanuts and three pounds of cashews cost $17.50. So:
[tex]2p+3c=17.5[/tex]
Five pounds of peanuts and two pounds of cashews cost $19.00. So:
[tex]5p+2c=19[/tex]
This yields a system of equations.
We can solve this using elimination. We can multiply the first equation by -5, and the second by 2. Therefore:
[tex]-5(2p+3c)=-5(17.5)[/tex]
Multiply:
[tex]-10p-15c=-87.5[/tex]
And:
[tex]2(5p+2c)=2(19)[/tex]
Multiply:
[tex]10p+4c=38[/tex]
Now, we can add the two equations together:
[tex](-10p-15c)+(10p+4c)=(-87.5+38)[/tex]
Combine like terms:
[tex]-11c=-49.5[/tex]
Therefore:
[tex]c=4.5[/tex]
So, a pound of cashews costs $4.50.
Our answer is C.
Notes:
To solve for the cost for peanuts, we can use the first (or second equation) again:
[tex]2p+3c=17.5[/tex]
Substitute:
[tex]2p+3(4.5)=17.5[/tex]
Solve for p:
[tex]2p+13.5=17.5\Rightarrow 2p=4\Rightarrow p=2[/tex]
So, a pound of peanutes cost $2.00.
