Question

The price of 3 pairs of skis and 4 pairs of skates was $470. What is the price of a pair of skis and a pair of skates if the price of 2 pairs of skates is $10 more than the price of a pair of skis?

Answer 1

Let the price of a pair of skis = x , and the price of a pair of skates = y

The price of 3 pairs of skis and 4 pairs of skates was $470
∴ 3x + 4y = 470  ⇒⇒⇒ (1)

The price of 2 pairs of skates is $10 more than the price of a pair of skis
∴ 2y - x = 10  ⇒⇒⇒ (2)

multiplying equation (2) by 3 and add to equation (1)
∴ 10y = 500
∴  y = 50

Substituting at (2) to find x
∴ x = 2y - 10 = 90

The price of a pair of skis = 90
The price of a pair of skates = 50

Answer 2

The price of a pair of skis is $90 and a pair of skates $50.

Given that

The price of 3 pairs of skis and 4 pairs of skates was $470.

We have to determine

What is the price of a pair of skis and a pair of skates if the price of 2 pairs of skates is $10 more than the price of a pair of skis?

According to the question

Let the price of the pairs of skis be x,

And the price of the pair of skates is y.

The price of 3 pairs of skis and 4 pairs of skates was $470.

$\rm 3x + 4y = 470$

If the price of 2 pairs of skates is $10 more than the price of a pair of skis.

$\rm 2y - x = 10$

On solving both the equations

From equation 2;

$\rm 2y - x = 10\\ \\ 2y-10=x\\ \\ x = 2y-10$

Substitute the value of x in equation 1.

$\rm 3x + 4y = 470\\ \\ 3(2y-10) +4y = 470\\ \\ 6y - 30 +4y = 470\\ \\ 10y = 470+30\\ \\ 10y=500\\ \\ y = \dfrac{500}{10}\\ \\ y = 50$

Substitute the value of y in equation 2,

$\rm 2y-x=10\\ \\ 2(50)-x=10\\ \\ 100-x=10\\ \\ -x=10-100\\ \\ -x=-90\\ \\ x=90$

Hence, the price of a pair of skis is $90 and a pair of skates $50.

To know more about System of Equation click the link given below.

https://brainly.com/question/724536