1. Read the problem carefully
2. Reread the problem and define the variable
3. Write an equations that represents the given situation
4. Solve the equation to find the unknown(s)
5. Check the results and answer the problem

The sum of 38 and twice a number is 124. Find the number.

Step 1: Read the problem

Step 2: Reread the problem and define the variable

Since we don't know what "the number" is we can just call it x.

Step 3: Write an equation that represents the given situation

We have to make sure that we follow the "instructions" give us in the problem.

We have to start from the very simple core of the problem. It talks about the number first with twice. When we talk about twice a number, we are talking about multiplying it by 2. So, that means that the first part of the equation is going to be 2x.

Now, after that, we see that we are going to take the sum of that and 38. Since a sum is when you add things, we are going to change our equation to 2x + 38.

Finally, all of that is going to be 124. When we talking about is, we can also say that it is equal to. So, the sum of 38 and twice a number (2x+38) is (=) 124. Our new, and final, equation is going to be 2x+38 = 124

Step 4: Solve the equation to find the unknown

Now that we have our equation, we can work on solving it.

2x + 38 = 124 (original equation)

2x = 86 (subtract 38 from both sides)

x = 43 (divide both sides by 2 to get the final answer)

Step 5: Check the results and answer the problem

Plug the number back into the original equation to make sure that the solution is correct.

2(43) + 38 = 124

86 + 38 = 124

124 = 124

Since we were able to get both sides of the equation to equal the same thing, then we have our solution.

Natalie owns a coffee shop. In her shop there are many varieties of coffee. One, an Ethiopian coffee sells for $7 per pound, and a second, a Colombian coffee, sells for $4 per pound. She’s found that some of her customers like a blend of the Ethiopian coffee and Colombian coffee. How much of each type of coffee should she mix to get 12 pounds of a mixture that sells for $6 per pound? Note: the price per pound of the mix is given, NOT the total value.

For the set up of this problem, we can work start with creating a table to organize the data.

Now we can set up the equations. We have to look at each of the columns. The only ones that can have a total value are the last two columns, the individual amount and the total value. Now we have to figure out how to write the equations. When we're talking about the individual amounts, we know that we have to add amounts from the both of the coffees in order to find the amount for the mix, so one equation that we have is x + y = 12. For the second equation, we can do a very similar process and add the values for the coffees and set the equal to the mix to get 7x + 4y = 6(12)

So, our two equations are:

• x + y = 12
• 7x + 4y = 72