Hippocampus Algebra: Solving problems with multiple steps

[Print]

The previous lesson involved solving multi-step equations. Let’s do a quick review, as we will be using what we learned in today’s lesson.

Click the “Submit” button after entering your answer.

Now, let’s begin today’s lesson, which deals with solving multi-step word problems.

Grant High School had a three-day bake sale.

The profit made during the first day is represented by the variable p.

The profit made during the second day of the sale was 15 dollars less than that on the first day. We write this as: p - 15

The profit made during the third day of the sale was 12 dollars less than that on the first day. We write this as: p - 12

The total profit made during the three-day sale was 63 dollars. We wish to find actual dollar profit for each day. We do this by determining the value of p.

Which of the following is an equation we can use to determine the value of p? Click the “Submit” button after selecting your answer.

We have our equation: p + (p – 15) + (p – 12) = 63. Now, we need to simplify it.

We do so by combining the like terms on the left-hand side of the equation.

We work backward to solve the equation. First, we apply the addition property of equality to undo the subtraction. We add 27 to both sides.

Next, we apply the division property of equality to undo the multiplication and isolate the variable p.

The result is: p = 30. We find that a 30 dollar profit was made on the first day, a 15 dollar profit was made on the second day, and an 18 dollar profit was made on the third day.

Here’s another example. Suppose we wish to make a rectangular garden that is surrounded by a total of 13 meters of fence.

The garden is to have a length of 5 meters.

We need to determine the width of the garden, which we represent by the variable x.

Which of the following is an equation we can write in order to solve for the length x? Click the “Submit” button after selecting your answer.

Now, we have an equation we can use to solve for the garden width: 2(x + 5) = 13.

However, we need to simplify the expression on the left-hand side by using the distributive property. This gives: 2x + 10 = 13

Solving the resulting equation requires two steps to solve it.

Which of the following is the first step we should take to solve the equation? Click the “Submit” button after selecting your answer.

Working backwards, we apply the subtraction property of equality by subtracting 10 from both sides. The result is: 2x = 3

Which of the following is the next step we should take to solve the equation? Click the “Submit” button after selecting your answer.

The final step involves using the division property of equality. We divide both sides by 2.

This gives us the solution: x = 1.5. The garden is one and a half meters wide.

We can check our work by substituting the solution into the original equation. We see that the left-hand expression is indeed equal to 13.

Now, let’s solve one more problem. Carlos went shopping for a new car. He found a nice model on sale with a zero percent loan.

The total cost of the car is $20,000.

Carlos plans to make a down payment of $2000.

He wants to pay off the remaining cost of the car with equal monthly payments of $500.

Let’s let n equal the total number of monthly payments Carlos will make.

How many monthly payments will Carlos need to make in order to pay off the car? Click the “Submit” button after entering your answer.

We write an equation by setting the total payments equal to the total cost of the car: 500n + 2000 = 20000. We solve it by using the subtraction and division properties. The result is: n = 36.

We can check the result by substituting the value of n back into the original equation.

We see that after Carlos makes a down payment of $2000, he will have to make 36 payments of $500 each to pay off remaining amount of the car’s cost.