Question

One day a store sells 30 sweatshirts. white ones cost $9.95 and yellow ones cost $10.50. in all, $310.60 worth of sweatshirts were sold. How many of each color were sold?

Answer 1

By setting up two equations, you are able to find out that the shop sold 8 white shirts and 22 yellow shirts.

Explanation:

From the description, you can make two equations with two unknown variables, which is just fun to solve!

Let's name the amount of white shirts sold for `x` and yellow ones for `y`.

Since the store sold 30 shirts, that means `x + y = 30`.

You also know how much the different shirts cost, and how much the shop earned that day.

`9.95x + 10.50y = 310.60`

So now, we have two different equations;

`1: x + y = 30`
`2: 9.95x + 10.50y = 310.60`

Rewrite equation 1 to:
`x = 30 - y`

Put this x-value in the second equation:
`9.95(30-y) + 10.50y = 310.60`
`298.50 - 9.95y + 10.50y = 310.60`
`0.55y = 310.60 - 298.50`
`0.55y = 12,1`

Divide both equations by 0.55

`y = 22` , this means that the shop sold 22 yellow shirts.
And since the shop sold a total of 30 shirts, you know that white shirts sold, `x = 30 - 22 = 8`

Summary:
- Set up two equations
`1 : x + y = 30`
`2: 9.95x + 10.50y = 310.60`

• Rewrite an equation so it only has one variable in it
• Insert that equation into the other one
• Solve it like an ordinary equation

Answer 2

white shirts = 8 and yellow shirts = 22

Explanation:

Let white sweat shirts be w
Let yellow sweat shirts be y

Condition 1:`-> " count"`

`y+w = 30` .............................(1)

Condition 2: `-> " cost"`

`10.5y +9.95w =310.6`............(2)

Method:
Use equation 1 to be the source of expressing one variable in terms of the other. Substitute into equation (2) so that it has only one variable then solve for that variable. Once found it can then be substituted back into (1) to solve for the other one.

From equation (1) `w = 30-y`....... (3)
Substitute (3) into (2) giving

`10.5y +9.95(30-y) =310.6`

`10.5y-9.95y+298.5=310.6`
`0.55y =310.6-298.5`
`y=22` ................................(4)

Substitute in (1) using (4)
`22+w=30`
`w=8`

Check using (2)
`10.5(22)+9.95(8) =310.6` Check confirms the values.

So white shirts = 8 and yellow shirts = 22