Answer:
$100
Step-by-step 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.
Answer: A pair of boots cost $100
Step-by-step 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
