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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The answer is x=−4 and y=−3
A. Add one more than was added to the previous number.
b. Divide by 2 each time.
c. Multiply by 3 each time.
d. Beginning is subtract one more than previously subtracted but the last two(15,,21) don’t fit the pattern.
These are three linear equations in in three variables.
To solve this by elimination, we are going to add equation (3) to (1) and (2) simultaneously.
First equation (3) + (1)
This implies that
Next let's add equation (2) and (3)
This implies that
Equations (4) and (5) are simultaneous linear equation in two variables.
Equation (4) ×2
This implies that
Also equation (5) ×5
This implies that
Now equation (7) - (6) gives
Substitute
in equations (6) or (7) and solve for y.
So using equation (6),
Now plug in z=0 and y=1 into (3) or any other containing the three variables and solve for x.
Hence