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?
Responses
$2.00
$2.00
$3.80
$3.80
$4.50
$4.50
$8.75
$8.75
We can set up a system of equations to solve this problem.
Let's say the price per pound for peanuts is x, and the price per pound for cashews is y.
From the first statement, we know that:
2x + 3y = 17.50
From the second statement, we know that:
5x + 2y = 19.00
To find the price per pound for cashews, we need to solve for y. We can first isolate y in the second equation:
2y = 19 - 5x
y = (19 - 5x)/2
Now we can substitute this expression for y into the first equation:
2x + 3((19 - 5x)/2) = 17.50
Simplifying this equation gives:
2x + (57 - 15x)/2 = 17.50
Multiplying every term by 2 to get rid of the fraction gives:
4x + 57 - 15x = 35
Combining like terms gives:
-11x + 57 = 35
Subtracting 57 from both sides gives:
-11x = -22
Dividing both sides by -11 gives:
x = 2
So, the price per pound for peanuts is $2.00.
Now we can substitute this value for x into the expression for y:
y = (19 - 5(2))/2
y = 9/2
So, the price per pound for cashews is $4.50.
Therefore, the correct answer is $4.50.