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Question

A sandwich shop is ordering apples and grapes to make chicken salad apples cost $1.25 per pound and grapes cost two dollars and.06D cents per pound if they order a total of 20 pounds of apples and grapes and paid $35.80 how many pounds of grapes did they order

Answer 1

Hey Fernanda!

This is actually not a differential equations problem, which is based on calculus, but more of an algebra problem. To solve these problems I always list out what the problem tells me. In this case:

apples cost 1.25 $ / lb

grapes cost 2.06 $ / lb

They ordered 20 lbs combined

Total cost $35.80

So how do we use this information to solve the problem? We need to make an equation to solve, but what is the equation? Well, we need to have an equation to relates amounts of apples and grapes bought to their total combined price. Think of this like being at a grocery store: you would get your total by multiplying some number of pounds by the cost of each fruit and then adding them up. So:

total cost = (apples cost per pound) * (number of pounds of apples) + (grapes cost per pound) * (number of pounds of grapes)

Some of these values we know and can plug in:

$35.80 = $1.25 * (pounds of apples) + $2.06 * (pounds of grapes)

If we let:

pounds of apples = a

pounds of grapes = g

Then we have:

$35.80 = $1.25 a + $2.06 g

35.80 = 1.25a + 2.06g

This gives us our first equation but we need a second to be able to solve for two variables. This equation is easier to come up with since we can make an equation for the total weight of the purchase.

Total weight = (weight of first item) + (weight of second item)

Total lbs = (lbs of apples) + (lbs of grapes)

20 = a + g

This gives us our second equation. Now you can use the method of substitution to solve the system of equations:

20 = a + g

35.80 = 1.25a + 2.06g

I'll let you finish the computations on this. Hope this helps clear up the problem!

-Nathan