35.5k views
1 vote
Tristan paid $17.50 to buy 2 pounds of peanuts and 3 pounds of cashews. Rivka paid $19.00 to buy 5 pounds of peanuts and 2 pounds of cashews. If both people paid the same price per pound, what was the price per pound for the cashews?

A. $2.00

B. $3.80

C. $4.50

D. $8.75

User Leyton
by
5.0k points

2 Answers

2 votes

Answer:

C. $4.50

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

:

---------

Cashews are $4.50 per pound

--------------

:have a great day.

User Birante
by
5.7k points
7 votes

Answer:

C

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:


2p+3c=17.5

Five pounds of peanuts and two pounds of cashews cost $19.00. So:


5p+2c=19

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:


-5(2p+3c)=-5(17.5)

Multiply:


-10p-15c=-87.5

And:


2(5p+2c)=2(19)

Multiply:


10p+4c=38

Now, we can add the two equations together:


(-10p-15c)+(10p+4c)=(-87.5+38)

Combine like terms:


-11c=-49.5

Therefore:


c=4.5

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:


2p+3c=17.5

Substitute:


2p+3(4.5)=17.5

Solve for p:


2p+13.5=17.5\Rightarrow 2p=4\Rightarrow p=2

So, a pound of peanutes cost $2.00.

User Cedric Arnould
by
5.3k points