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Five hats and three shirts cost $176. Three hats and five shirts cost $208. What is the cost of one hat?

The cost of one hat is __ dollars.

Respuesta :

Kakitzu

Let hats be x

Let shirts be y

We can set up a system of equations to figure out the cost of one hat.

5x+3y = 176 and 3x+5y = 208

Since we are finding the cost of the hats, we will need to isolate x from the equation. We can first get rid of y. One way we can do that is by multiplying the first equation with 5 and the second one with -3, effectively making y add up to 0 when we solve for x.

5(5x+3y = 176) --> 25x+15y = 880

-3(3x+5y = 208) --> -9x-15y = -624

We can now add the 2 equations together and solve for x.
25x+15y = 880

-9x-15y = -624

+>>>>>>>>>>>>>>>

16x = 256

x = 16

So the the cost of one hat is 16 dollars.

semsee45

Answer:

$16

Step-by-step explanation:

Define the variables:

  • Let x = cost of one hat
  • Let y = cost of one shirt

Create two equations using the defined variables and the given information.

Equation 1

Five hats and three shirts cost $176.

⇒ 5x + 3y = 176

Equation 2

Three hats and five shirts cost $208.

⇒ 3x + 5y = 208

Rewrite Equation 2 to make y the subject:

[tex]\implies \sf 3x+5y-3x=208-3x[/tex]

[tex]\implies \sf 5y=208-3x[/tex]

[tex]\implies \sf \dfrac{5y}{5}=\dfrac{208-3x}{5}[/tex]

[tex]\implies \sf y=\dfrac{208-3x}{5}[/tex]

Substitute the found expression for y into Equation 1 and solve for x:

[tex]\implies \sf 5x+3\left(\dfrac{208-3x}{5} \right)=176[/tex]

[tex]\implies \sf 5x+\dfrac{624-9x}{5}=176[/tex]

[tex]\implies \sf 5x+124.8-1.8x=176[/tex]

[tex]\implies \sf 3.2x+124.8=176[/tex]

[tex]\implies \sf 3.2x+124.8-124.8=176-124.8[/tex]

[tex]\implies \sf 3.2x=51.2[/tex]

[tex]\implies \sf \dfrac{3.2x}{3.2}=\dfrac{51.2}{3.2}[/tex]

[tex]\implies \sf x=16[/tex]

Therefore, the cost of one hat is 16 dollars.

Learn more about systems of equations here:

https://brainly.com/question/28093918

https://brainly.com/question/21447811

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