Question

At a sale on winter clothing, Cody bought two pairs of gloves and four hats for $43.00. Tori bought two pairs of gloves and two hats for $30.00. What were the prices for the gloves and hats?

Answer 1

Let g = number of gloves and let h = number of hats. We're going to write a system of equations.
2g+4h=43
2g+2h=30
Now I'm going to isolate a variable in one of the equations. Let's isolate the g in the second equation
g+h=15
g=15-h
Next, I'm going to plug in my new equation for g into the first equation and solve for h.
2(15-h)+4h=43
30-2h+4h=43
30+2h=43
2h=13
h=6.5
Finally, I'm going to plug my solution for h into either equation (I'll use the second one) and solve for g.
2g+2(6.5)=30
2g+13=30
2g=17
g=8.5
If I want to double check my answers, I can plug both values into the first equation and see if I get 43. The hats are $6.50 and the gloves are $8.50.

Answer 2

Using algebraic equation, the price of the gloves is $8.50 and the price of the hats $6.50.

What is algebraic equation?

Algebraic equation is an "equation consists of numbers, variables and operation(+,-,×,÷), raising to the power and extraction of a root".

According to the question,

Cody bought two pairs of gloves and four hats for $43.00 and Tori bought two pairs of gloves and two hats for $30.00. The algebraic equation is

2x + 4y = 43      →(1)

2x + 2y = 30      →(2)

x + y = 15                     [Divide equation (2) by 2]

     y = 15 - x

2x + 4(15-x) = 30

2x + 60 - 4x = 43

               -2x = 43 - 60

               -2x = -17

                  x = 17/2 = 8.50

Substitute x = 8.50 in equation (2)

2 (8.50) + 2 y = 30

17 + 2y = 30

       2y = 30 - 17

        2y = 13

          y = 13/2 = 6.50

Hence, using algebraic equation, the price of the gloves is $8.50 and the price of the hats $6.50.

Learn more about algebraic equation here  

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