Question

At the local clothing store 3 similar shirts and 4 similar jackets cost $360. 1 shirt and 3 jackets cost $220. Find the cost of each shirt

Answer 1

To solve this problem, it is easiest to set up a system of equations. Let's let the variable s represent the cost of a shirt and the variable j represent the cost of jackets. According to the given information, we can set up the following equations (because cost multiplied by quantity yields price):

3s + 4j = 360

1s + 3j = 220

Next, we can manipulate the second equation so that it equals s in terms of j. We do this by subtracting 3j from both sides of the equation, as shown below:

s = 220 - 3j

After that, we should substitute in this value for the variable s in the first equation.

3(220-3j) + 4j = 360

Next, we should use the distributive property to simplify the left side of the equation.

660 - 9j + 4j = 360

Then, we should simplify the left side of the equation by combining like terms.

660 - 5j = 360

After, we can subtract 660 from both sides of the equation to get the variable term alone.

-5j = -300

Finally, we should divide both sides of the equation by -5 in order to get the variable j alone.

j = 60

Now that we know the value of the variable j, we should substitute this value into one of the original equations and solve using division and subtraction to isolate the variable.

3s + 4j = 360

3s + 4(60) = 360

3s + 240 = 360

3s = 120

s = 40

Therefore, the cost of one shirt is $40.

Hope this helps!