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3 years ago

Hats and mittens are on sale at the store! One woman was able to buy 5 hats and 4 pairs of mittens for $30.

Mathematics

1 answer:

morpeh [17]3 years ago

4 0

The price of one hat is $2 and price of one pair of mittens is $5.

Step-by-step explanation:

Let,

Price of one hat = x

Price of one pair of mittens = y

According to given statement;

5x+4y=30 Eqn 1

2x+3y=19 Eqn 2

Multiplying Eqn 1 by 2

$2(5x+4y=30)\\10x+8y=60\ \ \ \ Eqn\ 3$

Multiplying Eqn 2 by 5

$5(2x+3y=19)\\10x+15y=95\ \ \ \ Eqn\ 4$

Subtracting Eqn 3 from Eqn 4

$(10x+15y)-(10x+8y)=95-60\\10x+15y-10x-8y=35\\7y=35\\$

Dividing both sides by 7

$\frac{7y}{7}=\frac{35}{7}\\y=5$

Putting y=5 in Eqn 1

$5x+4(5)=30\\5x+20=30\\5x=30-20\\5x=10$

Dividing both sides by 5

$\frac{5x}{5}=\frac{10}{2}\\x=2$

The price of one hat is $2 and price of one pair of mittens is $5.

Keywords: linear equation, subtraction

Learn more about linear equations at:

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2 years ago

Jamie has a piece of wood that is 6/8 inches long. He cuts the wood into pieces that are ¼ inches long. How many pieces of wood

pashok25 [27]

Answer: three pieces.

The piece of wood is 6/8 inches long - this fraction can be simplified to 3/4 by dividing both the numerator and denominator by 2.

Thus, he cuts a piece of wood that is 3/4 inches long into 1/4 inch pieces.

1 goes into 3 three times, so the piece of wood can be cut into three 1/4-inch pieces.

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2 years ago

Read 2 more answers

At sunset the temperature was 4 dgrees. the next morning at sunset it was -7 degrees. what is the difference betweeen these temp

DedPeter [7]

The difference between these temperatures for the sunset is found as 11 degrees.

<h3>What is temperature difference?</h3>

In science, the term Delta T (ΔT) refers to the temperature between two measuring points. The temperature varies according to time and/or location.

Some key features regarding the temperature difference are-

Merus, for example, uses it to assess the effectiveness of such a heat exchanger.
Or to evaluate the effectiveness of a heating or cooling system.
A fourth letter of a Greek alphabet is, (Δ). Whereas is the capital letter symbol and the lower case letter.
The sign is also used in mathematics. Describes the "difference" between any two changeable quantities. T is a value in a process that represents a difference between two observed temperatures.

Now, according to the question;

Let the initial temperature be 'T' = 4 degrees.

Let the final temperature be 't' = -7 degrees.

Therefore, the temperature difference is;

ΔT = T - t

= 4 - (-7)

= 4 + 7

ΔT = 11

Therefore, the difference between these temperatures is 11 degrees.

To know more about the temperature difference, here

brainly.com/question/24746268

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