Question

Jonathan needs two different kinds of socks for school . A pair of gym socks costs $3 , and a pair of dress socks costs $5 . If he spent a total of $50 on socks , how many of each type of socks did he purchase if the total number of pairs of sock is 12 ?

Answer 1

g + d = 12....g = 12 - d
3g + 5d = 50

3(12 - d) + 5d = 50
36 - 3d + 5d = 50
-3d + 5d = 50 - 36
2d = 14
d = 14/2
d = 7

g + d = 12
g + 7 = 12
g= 12 - 7
g = 5

so he bought 5 pairs of gym socks (g) and 7 pairs of dress socks (d)

Answer 2

Answer:

Jonathan needs 7 pairs of dress socks and 5 pairs of gym socks.

Step-by-step explanation:

A system of linear equations is a set of two or more first degree equations, in which two or more variables are related.

In this case it is possible to propose a system of equations as follows:

First the variables are defined. Jonathan needs two different kinds of socks for school: A pair of gym socks and a pair of dress socks.  Then the variables are defined as:

• x:  Quantities of pairs of gym socks that Jonathan needs.
• y: Quantities of pairs of dress socks that Jonathan needs.

Then, defined the variables, the system equations are raised.

The total number of pairs of sock is 12. This means that the number of pairs of gym socks plus the number of pairs of dress socks is 12. Expressed by an equation this is: x+y=12 Equation (A)

On the other hand, a pair of gym socks costs $3 , and a pair of dress socks costs $5.  Then to calculate what is spent on each pair of socks, the corresponding price is multiplied by the quantities of every kind of pair of socks. And considering that he spent a total of $ 50, it is possible to determine the other equation necessary for the system by adding the amount spent to buy each kind of pair of socks he needs: 3*x+5*y=50 Equation (B)

So, the system of equations to solve is:

$\left \{ {{x+y=12} \atop {3*x+5*y=50}} \right.$

Solving a system of equations consists in finding the value of each variable so that all the system's equations are fulfilled.

One of the methods used to solve a system of equations is the substitution method. This method consists of isolating one of the unknowns (for example, x) and replacing its expression in the other equation.

In this case, you choose to isolate "x" from equation (A), leaving the expression: x=12-y Equation (C)

Replacing equation (C) in equation (B) you get:

3*(12-y)+5*y=50

Now this equation is solved:

3*12-3*y+5*y=50

36-3*y+5*y=50

36+2*y=50

2*y=50-36

2*y=14

y=14÷2

y=7

Remembering that "y" is the quantities of pairs of dress socks that Jonathan needs, so  it is possible to say that Jonathan needs 7 pairs of dress socks.

Now, replacing the value of "y" in equation (C) you get:

x=12-y

x=12-7

x=5

Remembering that "x" is the quantities of pairs of gym socks that Jonathan needs, so  it is possible to say that Jonathan needs 5 pairs of gym socks.