Question

Myra was given the following problem.

The Owens family has saved up $50,000 for a down payment on a house. They are
oing to use this money as the 10% down payment their lender is requiring them to
Le to purchase the house. What is the price of the house that the Owens family
is buying?
When Myra solved this problem, she decided to take 10% of $50,000, and she got an
answer of $5.000. She knows that this number is too low to be the price of a house.
Explain to Myra in your own words how to solve the problem correctly. You may
set up the equation any way you'd like to in your explanation, but you must include
a variable x that represents the total price of the house in your equation.

Answer 1

Equation: 10% * x = 50,000

Price: $500,000

Explanation:

It is important to understand what the problem is telling you, so you can answer it correctly. Myra took 10% of $50,000. Did the problem ask for that calculation? The answer is no. That is why after calculating 10% of $50,000 she has a number that has no meaning in this problem.

The family saved $50,000 for the down payment of a house.

The down payment is 10% of the price of the house.

We are trying to find the price of the house. We don't need to find 10% of $50,000. What we need to figure out is $50,000 is 10% of what number? 10% is 1/10, so $50,000 is 1/10 of a number that is much bigger than $50,000. Since $50,000 is 1/10 of the price, then the price is 10 times $50,000. 10 times $50,000 is $500,000. The price of the house is $500,000.

Now let's use an equation to solve the problem.

Let the actual price if the house be x, an unknown amount.

10% of x is $50,000.

Now we translate this into an equation.

10% is the same as 0.1

0.1 of x = 50,000

In math, the word "of" usually means a multiplication.

0.1 * x = 50,000

To solve for x, we divide both sides by 0.1

x = 50,000/0.1

x = 500,000

The price of the house is $500,000.