story problem

Question

Deshaun's Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee costs Deshaun
$5.80
per pound, and type B coffee costs
$4.35
per pound. This month, Deshaun made
145
pounds of the blend, for a total cost of
$716.30
. How many pounds of type A coffee did he use?

Answer 1

Answer: 59 lbs

 

Explanation: 

 

This is a classic problem that after some practice you'll start to recognize. It's a systems of equations problem, meaning you want to find a few questions within the story to describe the problem, and then use them to solve it.

 

Step 1: Recognize it's a systems of equations problem

A red flag went up for me that this was a systems of equations problem because 1) there are a variety items each with there own dollar amount and 2) a 'total' quantity was bought or sold (in this case bought by the coffee shop). So now it's about finding the equations that'll help us solve the problem.

 

Step 2: Find the equations

We need variables to represent what we are looking for, lbs of coffee. If we used 'a' and 'b' for coffee A and B respectively, we know that a + b = 145, because the story tells us that between coffee A and B, 145 pounds was made. So that's our first equation. 

 

A rule of systems of equations is that you need the same number of equations as you have unknowns to find all the unknowns. So since both 'a' and 'b' are unknown, we need our second equation to solve for them. 

 

The second one comes from the cost. We can write that 5.80a + 4.35b = 716.30 because the total amount we spend on coffee A (5.80 times the number of pounds of coffee A bought) plus the total amount we spend on coffee B (4.35 times the number of pounds of coffee B bought) will equal 716.30, the total spent on coffee. 

 

So we have both equations. Now to solve for 'a', pounds of coffee A used (or bought.. using that term interchangeably). 

 

Step 3: Solve using the equations

We want to put one variable in terms of another so we can then plug that into the more complicated equation to solve for one variable. Once we've solved for one, we can easily solve for the other. I won't go through every step, but here's the gist:

 

Write 'a + b = 145' as 'b = 145 - a'

Plug 'b' into the other equation --> 5.80a + 4.35(145 - a) = 716.30

Get 'a' into one term on the left side, move constants onto the right side -->  1.45a = 85.55

Solve for 'a' by dividing each side by 1.45 --> a = 59 lbs <-- your answer.