PLEASE help. Algebra one class. I need 2 equations and the cost per hat and glove

Question

At a sale on winter clothing, Amberlee bought two pairs of gloves and four hats for $48.50. Ryan

bought two pairs of gloves and two hats for $34.00. What were the prices for the gloves and hats?

Answer 1

Let g = the price of a pair of gloves and h = the price of a hat

From the description:

2g + 4h = 48.50

2g + 2h = 34.00

Subtract the second equation from the first and solve for h

2h = 14.50 --> h = $7.25

Substitute the value of h into the first equation and solve for g:

2g + 4(7.25) = 48.50

2g + 29 = 48.50

2g = 48,50-29 = 19.50

g = 19.5/2 = $9.75

The price of a pair of gloves is $9.75 and the price of a hat is $7.25.

Answer 2

First, we need to express what each person bought with an equation. Let's have the number of gloves = x, and the number of hats = y.

The first person bought two pairs of gloves and four hats for $48.50, so 2x + 4y = 48.50

The second person bought two pairs of gloves and two hats for $34.50, so 2x + 2y = 34.00

Now, we need to get one of the variables on its own for both equations. Let's go with x. After some rearranging, the equations now look like this:

x = (48.50 - 4y)/2 and...

x = (34.00 - 2y)/2

Now we can set the equations equal to each other and solve for y, so...

(48.50 - 4y)/2 = (34.00 - 2y)/2 -----> 97 - 8y = 68-4y ----> 29 = 4y ----> y = 7.25

We now know that one hat costs $7.25. Now we simply plug this value into one of the original equations to solve for the cost of a pair of gloves.

2x +4(7.25) = 48.50 ----> 2x = 19.50 ----> x = 9.75

Now we know that a hat costs $9.75. You can now plug these values into the other original equation to check your work.

Hope this helps!! Let me know if you need any other help!

Answer 3

cost of glove = g

cost of hat = h

2 equations 2 unknowns:

1) 2*g + 4*h = $48.50

2) 2*g + 2*h = $34.00 can rearrange to g = $17.00 - h and plug into first equation

2($17.00 - h) + 4*h = $48.50

$34.00 + 2*h - 4*h = $48.50

2*h = $14.5

h = $7.25 plug this into g = $17.00 - h to get g = $9.75

double check with equations 1 and 2

1) 2*g + 4*h = 2 (9.75) + 4 (7.25) = $48.50

2) 2*g + 2*h = 2 (9.75) + 2 (7.25) = $34.00

Therefore : cost of glove = g = $9.75

cost of hat = h = $7.25