Question

3x+5y=60 solve for y

Answer 1

You originally have x colored pencils in your pencil box. You share them equally between you and your friend. You add in 3 more colored pencils to your own box after sharing them. This gives you a total of 15 pencils.

a) Write an equation and show all of your steps for solving x (the original number of pencils in your box)

b) What if you wanted to have at least 20 pencils left in your box? How many pencils would you have needed originally?

c) Write an inequality and show all steps for solving for x.

(5 points)

Answer 2

To solve for y, we need to isolate it on one side of the equation.

The given equation is 3x + 5y = 60.

To do this, let's start by subtracting 3x from both sides:

3x + 5y - 3x = 60 - 3x

This simplifies to:

5y = 60 - 3x

Next, let's divide both sides by 5 to solve for y:

5y/5 = (60 - 3x)/5

This results in:

y = (60 - 3x)/5

Therefore, the solution for y is y = (60 - 3x)/5.

Answer 3

a) Let x be the original number of colored pencils in your box. After sharing them equally with your friend, you each have x/2 colored pencils. Then, after adding 3 more colored pencils to your own box, you have x/2 + 3 colored pencils.

Putting all the information together, we can write the equation:

x/2 + 3 = 15

To solve for x, let's begin by subtracting 3 from both sides:

x/2 = 12

Next, multiply both sides by 2 to isolate x:

x = 24

Therefore, the original number of pencils in your box was 24.

b) To find out how many pencils you would have needed originally to have at least 20 left in your box, we can set up the equation:

x/2 + 3 ≥ 20

Subtract 3 from both sides:

x/2 ≥ 17

To isolate x, multiply both sides by 2:

x ≥ 34

Therefore, you would have needed at least 34 colored pencils originally to have at least 20 pencils left in your box.

c) The inequality for this situation is:

x/2 + 3 ≥ 20

To solve for x, let's begin by subtracting 3 from both sides:

x/2 ≥ 17

Next, multiply both sides by 2 to isolate x:

x ≥ 34

Therefore, the solution to the inequality is x ≥ 34.