Matthew has 30 Starbursts. Twelve are yellow and the rest are red. What is the ratio of yellow starbursts to red?

Anestetic [448]

First we distribute $\frac{1}{5}$ into $n$ and $-\frac{1}{7}$ .

$\frac{1}{5} * n = \frac{1}{5} n$
$\frac{1}{5} * -\frac{1}{7} = - \frac{1}{35}$

That makes the left side of the equation

$\frac{1}{5} n - \frac{1}{35} = \frac{1}{6} n$

Now we subtract $\frac{1}{5}n$ from $\frac{1}{6} n$ , which makes $\frac{1}{30}$

Now the equation is

$-\frac{1}{35} = -\frac{1}{30n}$

Our goal is to isolate $n$ , so we both sides by 30

$30* -\frac{1}{35} = - \frac{1}{30}n * 30$

That will make the equation

$- \frac{30}{35} = -n$

We multiply -1 on both sides of the equation:

$\frac{30}{35} = n$

Finally we simplify $\frac{30}{35}$ , which makes $\frac{6}{7}$

So the answer is $n = \frac{6}{7}$

5 0

3 years ago

Last month, Stephen neighbors paid him to take care of their fish when they went on vacation. HeHe spent $5 of his earnings on

Ira Lisetskai [31]

Answer:

Stephen's neighbors paid Stephen no more that $28.

Step-by-step explanation:

Given:

Stephen spent $5 of his earnings on snack.

He spent $17 in a new book.

He is left with no more than $6 left.

To describe how much Stephen's neighbors paid him.

Solution:

Let Stephen's earnings in dollars be = $x$

Amount left after spending on snacks in dollars = $x-5$

Amount left after spending on a new book in dollars = $x-5-17$ = $x-22$

The amount remaining is no more than $6.

Thus, the inequality representing the situation can be given as:

$x-22\leq6$

Solving for $x$

Adding 22 both sides.

$x-22+22\leq6+22$

$x\leq 28$

Thus, Stephen's neighbors paid Stephen no more that $28.

3 0

3 years ago

K12 5 GRADE WORK NEED HELP MARK CROWN

Dvinal [7]

Answer:

6.85 oz

Step-by-step explanation:

13.7 ÷ 2 = 6.85

4 0

4 years ago

Read 2 more answers

Five times the difference of a number and 12 minus 4 times the same number is – 36. What is the equation?

Katen [24]

Answer:

(5x - 12) - 4x = -36

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers

Samantha divides $16,000 into three investments: a savings account 3 points paying 7% annual interest, a bond paying 9%, and a m

kipiarov [429]

Answer:

2000 was the amount of the investment in the savings account

6000 was the amount of the investment in the payment of bonds

8000 was the amount of the investment in the money market

Step-by-step explanation:

In this case, a system of equations must be generated with the information given in the statement.

Let x be the amount of the investment in the savings account

Let y be the amount of the investment in the payment of bonds

Let z be the amount of investment in the money market

Now, the first equation would be that of total investment:

x + y + z = 16000

The second equation is that of interest:

0.07 * x + 0.09 * y + 0.12 * z = 1640

Last, her equation has invested three times more in the bond payment than in the savings account:

3 * x = y

So we have 3 equation with 3 unknowns. Therefore there is a solution.

x + y + z = 16000

0.07 * x + 0.09 * y + 0.12 * z = 1640

3 * x = y

In order not to make the answer too extensive, we will solve the system of equations with the help of symbolab, here is the step-by-step of everything they do in a very detailed and precise way.

https://es.symbolab.com/solver/step-by-step/x%20%2B%20y%20%2B%20z%20%3D%2016000%3B%200.07%20%5Ccdot%20x%20%2B%200.09%20%5Ccdot%20y%20%2B%200.12%20%5Ccdot%20z%20%3D%201640%3B%203%20%5Ccdot%20x%20%3D%20y

From this, the results are as follows:

x = 2000

y = 6000

z = 8000

Thus

2000 was the amount of the investment in the savings account

6000 was the amount of the investment in the payment of bonds

8000 was the amount of the investment in the money market

7 0

3 years ago