Question

A store sells ink jet printers and laser printers. On Monday, it sold a total of 100 printers. The store earns $40 profit for each ink jet printer sold and $55 profit for each laser printer sold. If the store's profits from printer sales were $4,600 on Monday, how many more ink jet printers were sold than laser printers?

Answer 1

No ink jet printers were sold. 107 more laser printers were sold than ink jet printers.

Step-by-step explanation:

To find the number of ink jet printers sold, we can set up a system of equations. Let x be the number of ink jet printers sold, and y be the number of laser printers sold. We can then create the following equations:

x + y = 100 (equation 1)

40x + 55y = 4600 (equation 2)

We can solve this system of equations using substitution or elimination. Let's use the method of elimination:

Multiplying equation 1 by 40, we get: 40x + 40y = 4000 (equation 3)

Subtracting equation 3 from equation 2, we get: 15y = 1600

Dividing both sides by 15, we get: y = 1600/15 = 106.67

Since the number of printers must be a whole number, we know that 107 laser printers were sold. Substituting this into equation 1, we can find the number of ink jet printers: x + 107 = 100 => x = 100 - 107 = -7

Solving for x, we find that -7 ink jet printers were sold. However, since the number of printers cannot be negative, we can conclude that no ink jet printers were sold.

Therefore, 107 more laser printers were sold than ink jet printers.

Answer 2

The store sold 20 more ink jet printers than laser printers.

Step-by-step explanation:

Since the store sold 100 printers, you can say that the result of adding up the numbers of each type of printers sold is equal to 100, which is:

x+y=100, where:

x is the number of ink jet printers sold

y is the number of laser printers sold

Also, you know the amount the profit the store gets for each type of printer and the total profit received on Monday which means that adding up the results of multiplying each type of printer for its price is equal to the total profit, which can be expressed as:

40x+55y=4,600

Now, you have two equations:

x+y=100 (1)

40x+55y=4,600 (2)

You have solve this system of equations to find the number of ink jet and laser printers that were sold. First, you have to solve for x in (1):

x=100-y (3)

Then, you have to replace (3) in (2) and solve for y:

40(100-y)+55y=4,600

4000-40y+55y=4,600

15y=600

y=600/15

y=40

Finally, you can replace the value of y in (3) to find the value of x:

x=100-40

x=60

Now that you know that the store sold 60 ink jet printers and 40 laser printers, you can find the difference between this numbers to be able to know how many more ink jet printers were sold:

60-40=20

According to this, the answer is that the store sold 20 more ink jet printers than laser printers.