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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Answer:
There are N students in the class.
We know that ONLY ONE of the inequalities is true:
N < 10
N > 10
N < 22
N > 22
We want only one of these four inequalities to be true.
Remember that if we have:
x > y
y is not a solution, because:
y > y is false.
Then:
If we take N = 10, then:
N < 22
Is the only true option.
While if we take N = 22
N > 10
is the only true option.
So there are two possible values of N.
Answer:
Step-by-step explanation:
the line grath is your answer
YOU WELCOME
Answer:
N=250
Step-by-step explanation:
"twice as many nickels as dimes" means N =2D [eq1]
"collection of nickels and dimes is worth $25" means
5N + 10D = 2500 [eq2]
(To avoid using decimal points, PLZ express everything in cents.)
Substitution (substitute N from eq1 into eq2]:
5(2D) + 10D = 2500
10D + 10D = 2500
20D = 2500
D = 125
N=2D [eq1 again]
N=2(125)
N=250
Check:
Is 5(250) + 10(125) = 2500 ?
1250 + 1250 = 2500 ?
2500 = 2500 ?yes
