The price of one hat is $2 and one pair of mittens is $5
Step-by-step explanation:
Hats and mittens are on sale at the store!
- One woman was able to buy 5 hats and 4 pairs of mittens for $30
- Another woman purchased 3 pairs of mittens and 2 hats for $19
- The price of one hat is x
- The price of one pair of mittens is y
We need to find x and y
∵ One woman was able to buy 5 hats and 4 pairs of mittens for $30
∵ The price of one hat is x
∵ The price of one pair of mittens is y
- Multiply 5 hats by x and 4 pairs of mittens by y and equate
their sum by 30
∴ 5x + 4y = 30 ⇒ (1)
∵ Another woman purchased 3 pairs of mittens and 2 hats for $19
- Multiply 2 hats by x and 3 pairs of mittens by y and equate
their sum by 19
∴ 2x + 3y = 19 ⇒ (2)
Now we have a system of equations to solve it
Multiply equation (1) by -2 and equation (2) by 5 to eliminate x
∵ -10x - 8y = -60 ⇒ (3)
∵ 10x + 15y = 95 ⇒ (4)
- Add equations (3) and (4)
∴ 7y = 35
- Divide both sides by 7
∴ y = 5
Substitute the value of y in equation (1) or (2) to find x
∵ 2x + 3(5) = 19
∴ 2x + 15 = 19
- Subtract 15 from both sides
∴ 2x = 4
- Divide both sides by 2
∴ x = 2
The price of one hat is $2 and one pair of mittens is $5
Learn more:
You can learn more about the system of equations in brainly.com/question/2115716
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9514 1404 393
Answer:
(x, y) = (-5, -6)
Step-by-step explanation:
The coefficients of y are the same, so we can eliminate y by subtracting one equation from the other. Here, we choose to subtract the first from the second, so that the coefficient of x ends up positive.
(-5x +5y) -(-6x +5y) = (-5) -(0)
x = -5 . . . . . . simplify
-6(-5) +5y = 0 . . . . . . substitute x into the first equation
6 +y = 0 . . . . . . . . . . divide by 5
y = -6 . . . . . . subtract 6
The solution to the system of equations is (x, y) = (-5, -6).
Answer:
$465 at Back Street
$515 at Main Street
Step-by-step explanation:
980 (total) - 50 (the difference between the two) = 930
930/2 = 465 (back street)
465 + 50 (the difference) = 515 ( main street)
CHECK: 465 + 515 = 980
Answer:
13: 10
21: 20
29: 30
Step-by-step explanation:
Just draw three rectangles and a half of one
