Question

a shoe store sells nike amd adidas shoes. joan pays $800 for 3 pairs of adidas shoes and 4 nikes shoes. chris pays $350 for 1 pair of adidas and 2 Pair of nikes shoes. write a system of linear equation that represents this situation. what is the price of one pair of nike?

Answer 1

To determine the price of one pair of Nike shoes, a system of two linear equations was formed: 3A + 4N = 800 and A + 2N = 350. By solving the system, we found that the price of one pair of Nike shoes is $125.

Step-by-step explanation:

To create a system of linear equations to represent the situation of buying Adidas and Nike shoes at a shoe store, we need to use two variables to represent the price of each pair of Adidas shoes (A) and Nike shoes (N). Based on the information given:

Joan pays $800 for 3 pairs of Adidas shoes and 4 pairs of Nike shoes, which can be represented as the equation 3A + 4N = 800.

Chris pays $350 for 1 pair of Adidas and 2 pairs of Nike shoes, which can be represented as the equation A + 2N = 350.

To find the price of one pair of Nike shoes, we can solve the system of equations. By subtracting the second equation from the first (multiplied by 3), we eliminate variable A:

1. (3A + 4N) - 3(A + 2N) = 800 - 3(350)
2. 3A + 4N - 3A - 6N = 800 - 1050
3. -2N = -250
4. N = $125

Hence, the price of one pair of Nike shoes is $125.

Answer 2

The Nikes cost $125.

The Adidas cost $100

Step-by-step explanation:

Let :

• a = # of adidas shoes
• n = # of nike shoes

`\left \{ {{3a + 4n = 800} \atop {a + 2n = 350}} \right.`

Solve the bottom equation for a:

• a + 2n = 350
• a = 350 - 2n

Now substitute this for a in the top equation:

• 3a + 4n = 800
• 3(350 - 2n) + 4n = 800
• 1050 - 6n + 4n = 800
• 1050 - 2n = 800
• -2n = -250
• n = 125

The Nikes costs $125.

We can also solve for the Adidas:

Use the previous equation we made:

• a = 350 - 2n
• a = 350 - 2(125)
• a = 350 - 250
• a = 100

The Adidas costs $100

-Chetan K