Help me solve my math word problem please and thank you

Question

at a sale on winter clothing, ethan bought two pairs of gloves and four hats for $43. melanie bought two pairs of gloves and two hats $30. what is the cost for the gloves and hats

Answer 1

Hi Karen,

 

Let's begin by assigning letters to represent our two unknowns:

    x = cost of a pair of gloves

    y = cost of a hat

 

Now let's write equations using our unknowns to represent the total cost for each given purchase:

    2x + 4y = 43 (Ethan's purchase)

    2x + 2y = 30 (Melanie's purchase)

 

Next, we'll group our equations together and use them to solve for our two unknowns (x and y):

 

    Equation #1:  2x + 4y = 43 (Ethan's purchase)

    Equation #2:  2x + 2y = 30 (Melanie's purchase)

    Equation #3:         2y = 13 (Subtract #2 from #1)

                                 y = 13/2

                                 y = 6.50

    y = $6.50  (cost of a pair of gloves)

 

    Equation #2:  2x + 2y = 30 (Melanie's purchase)

                        2x + 2(6.50) = 30 (y value plug-in)

                        2x + 13 = 30

                                2x = 30 - 13

                                2x = 17

                                  x = 17/2

                                  x = 8.50

    x = $8.50 (cost of a hat)

 

Finally, we can check our answers by plugging them both back into our first equation to see if the equation proves true:

    Equation #1:  2x + 4y = 43 (Ethan's purchase)

                        2(8.50) + 4(6.50) = 43

                        17 + 26 = 43

                                43 = 43 (equation proven true)

 

Since our answers prove our first equation true, we are confident that our answers are correct.

 

Thanks for submitting this problem and glad to help.

 

God bless, Jordan.

Answer 2

2x + 4y = 43

2x + 2y = 30

 

Subtract the second from the first

 

2y = 13

y = 6.5

 

2x + 2(6.5) = 30

2x = 17

x = 8.5

 

Gloves are $8.50 and hats are $6.50