Question

Chris has $700 to spend at the mall. He could buy 2 pairs of boots and 5 outfits or 1 pair of boots and 6 outfits. How much does a pair of boots cost?

Answer 1

Answer: A pair of boots cost $100

Explanation:

Let x represent the cost of a pair of boots.

Let y represent the cost of an outfit.

Chris has $700 to spend at the mall. He could buy 2 pairs of boots and 5 outfits. This means that

2x + 5y = 700- - - - - - - - - - - - -1

He could also buy 1 pair of boots and 6 outfits for $700. It means that

x + 6y = 700 - - - - - - - - - - - -- -2

Multiplying equation 1 by 1 and equation 2 by 2, it becomes

2x + 5y = 700

2x + 12y = 1400

Subtracting, it becomes

- 7y = - 700

y = - 700/ -7

y = 100

Substituting y = 100 into equation 2, it becomes

x + 6 × 100 = 700

x + 600 = 700

x = 700 - 600

x = 100

Answer 2

$100

Explanation:

Assign variables for the cost of "boots" and "outfits"

let x be the cost of a pair of boots

let y be the cost of an outfit

Write equations to represent the problem

2x + 5y = 700 Two pairs of boots and five outfits

x + 6y = 700 One pair of boots and six outfits

Solve the system. I will use the substitution method. Rearrange the second equation to isolate "x".

x + 6y = 700

x = 700 - 6y I can replace "x" in the other equation with this expression

2x + 5y = 700 Substitute "x" with the expression

2(700 - 6y) + 5y = 700 Distribute over brackets with multiplication

1400 - 12y + 5y = 700 Collect like terms with "y"

1400 - 7y = 700 Start isolating "y"

1400 - 1400 - 7y = 700 - 1400 Subtract 1400 from both sides

-7y = -700

-7y/-7 = -700/-7 Divide both sides by -7

y = 100 Cost of an outfit

Now we find "x". Substitute the value of "y" into any equation we have used.

x = 700 - 6y

x = 700 - 6(100) Multiply

x = 700 - 600 Subtract

x = 100 Cost of a pair of boots

Therefore a pair of boots cost $100.