MATHEMATICS MIDDLE SCHOOL

Sarah bought 5 items for a total of $24. A bracelercosts $5 and a pair of sunglasses costs $4.50.
Write a system of equations and determine how
many of each item she purchased.
("Einstein" letters)

Answers

Answer 1

Answer:

Sarah bought 3 bracelets and 2 pairs of sunglasses.

Step-by-step explanation:

Total items bought = 5 items

Total spent = $24

Cost of one bracelet = $5

Cost of pair of sunglasses = $4.50

Let,

x be the number of bracelet bought.

y be the number of sunglasses bought.

According to given statement;

x+y=5 Eqn 1

5x+4.50y=24 Eqn 2

Multiplying Eqn 1 by 5

$5(x+y=5)\n5x+5y=25\ \ \ Eqn\ 3$

Subtracting Eqn 2 from Eqn 3

$(5x+5y)-(5x+4.50y)=25-24\n5x+5y-5x-4.50y=1\n0.50y=1$

Dividing both sides by 0.50

$(0.50y)/(0.50)=(1)/(0.50)\ny=2$

Putting in Eqn 1

$x+2=5\nx=5-2\nx=3$

Sarah bought 3 bracelets and 2 pairs of sunglasses.

Keywords: linear equations, subtraction

Learn more about subtraction at:

#LearnwithBrainly

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Need help on this problem

What does 3/8 x 4/9 mean?

Answers

3/8 × 4/9

First, let's see if they can cancel out. Nope. 3 and 8 have no common factors, and neither do 4 and 9.

When you're multiplying fractions together, you can switch out the numerators and denominators (if it helps you visualize things more easily. You won't need to do this step with some practice).

3/8 × 4/9 =
3/9 × 4/8 =

Now three 3 and 9 both have a common factor of 3. Divide them both by that common factor, top and bottom.

3/9 × 4/8 = //Comment: 3 ÷ 3 = 1, 9 ÷ 3 = 3.
1/3 × 4/8 =

4 and 8 likewise have a common factor, but of 4. Divide them both by that common factor. Remember, what you divide or multiply from the top, must also be done with the bottom and vice version. This way it will cancel out.

1/3 × 4/8 = //Comment: 4 ÷ 4 = 1, 8 ÷ 4 = 2.
1/3 × 1/2 =

Now multiply the numerators to each other, and the denominators to each other.

1/3 × 1/2 =
(1 × 1)/(3 × 2) =
1/(3 × 2) =
1/6

That is your answer. To check, we can do the opposite operation. In this case, you can divide the answer by either of the two original fractions and you should get the other. That's a little more advanced though, but a quick and easy way to convert from fraction division to fraction multiplication is to invert the fraction and the division sign to a multiplication sign.

1/6 ÷ 3/8 = 4/9 //Comment: Invert fraction and division sign.
1/6 × 8/3 = 4/9 //Can we cancel out any thing?
1/3 × 8/6 = 4/9

8 and 6 have a common factor of 2. Divide both by that factor.

1/3 × 8/6 = 4/9 //Comment: 8 ÷ 2 = 4, 6 ÷ 2 = 3
1/3 × 4/3 = 4/9

Multiply the numerators together and the denominators together.
1/3 × 4/3 = 4/9
(1 × 4)/(3 × 3) = 4/9
4/(3 × 3) = 4/9
4/9 = 4/9

4/9 = 4/9 which is true. If you like, try it out with 1/6 ÷ 4/9 :)

To find 45% of 72, multiply 45/100×72. Study the model: 45/100×72=3,240/100=32.4. Find 35% of 12.

Answers

You can also just multiply by the decimal equivalent.

12*.35=4.2

35% of 12 is 4.2

Hope this helps!

Answer:

4.2

Step-by-step explanation:

Find 35% of 12.

To find 35% of 12, you can use the method you demonstrated above by solve

35% = 35/100

of 12 = multiplication.

35/100 × 12

0.35 × 12

= 4.2

35 × 12/100

420/100

= 4.2

Hope this helps!

Thanks.

A graduated cylinder with a radius of 3 cm contains water to a height of 9 cm. Yann adds 15 steel balls, each with a diameter of 3 cm. What is the total volume of the contents in the cylinder after the balls are added? Use 3.14 to approximate pi and express your answer in hundredths.

Answers

find volume
Vcylinder=hpir^2

volume of cylinder=(4/3)pir^3

water to height of 9
radis i3
V=9*pi*3^3
V=81pi

the balls
15 of them
diameter/2=radius
3/2=1.5
radous=1.5
15V=15(4/3)(pi)(1.5^3)
15V=20pi(3.375)
15V=67.5pi

addd tehm

81pi+67.5pi=148.5pi
aprox pi=3.14
148.5*3.14=466.29 cm^3

Write the sum as a product of the gcf of the two numbers 75+90

Answers

Solutions

75:    3 5 5

90:   2 3 3 5

GCF:    3 * 5

= 15

What Fraction Is Bigger 8/15 or 14/25?

Answers

The first thing to do is to make the denominators the same:
8/15 = 40/75
14/25 = 42/75

42/75 is bigger than 40/75. Therefore, 14/25 is bigger than 8/15.

In order to solve these problems, you would have to change the fractions so that they have equal denominators. In order to do so, you must find the LCM of the denominators, in this case 15 and 25.

The LCM is 75 for these two numbers. Now, you change the fractions based on their new denominators.

8/15 = 40/75
14/25 = 42/75

I got this by dividing 75 by the previous denominators and multiplying that result by the original numerators. (i.e. 75/25 = 3 * 14 = 42)

So, now that you've changed both fractions to have equal denominators, you can see, by the numerators, which of the two is bigger.

Your answer is 14/25.

Hope this is clear and helps you out for future problems :)

Is 2/5 bigger than 40/ 100