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
#LearnwithBrainly
Answer:
Step-by-step explanation:
Given problems are absolute value problems, So we need to plug the values of given parameters and get the final result.
We have given here,
a =-2 , b = 3 , c = -4 and d = -6
Now we know that An absolute function always gives a positive value.
Let's apply this strategy in the given problems.
1. ║a+b║
Plug a= -2 and b = 3
We get, ║-2+3║=║1║= 1
2. 5║c+b║
Plug c= -4 and b=3
i.e. 5║-4 + 3║= 5║-1║=5×1 = 5
3. a+b║c║
Plug values a= -2 , b=3 and c=-4
i.e -2 +3║-4║ = -2 + 3×4 = -2 + 12 = 10
4. ║a+c║÷(-d)
i.e ║-2 + (-4)║÷(-6) = ║-6║÷(-6) = 6÷(-6) = -1
5. 3║a+d║+b
i.e 3║-2+(-6)║+3 = 3║-8║+3 = 3×8 +3 = 27
When y = 2, x = 8.
This can be written as: 2/8.
Simplified: 1/4
True
Answer:
C - 19/24
Step-by-step explanation:
Take the fractions and put the denominators into a common factor
Add Numerators Across
Take the square root of 256 to find the side length of the mirror
√256 =16
the rectangles width is 16, it length is 2 inches longer
16+2 =18 so the length is 18
to find the area multiply them together
18x16=288
the area is 288 inches² :)
