Isabel is saving money to buy a game. So far she has saved $36, which is three-fourths of the total cost of the game. How much does the game cost?

Answer 1

Hello! Let's see if I can help you understand the question and get to the right answer. It is somewhat difficult not knowing what you have learned so far, but let's try :)

So, Isabel is saving money for a game, but we don't know the total cost of the game. So we can use a letter, "x", to represent the total cost of the game.

What we do know is that so far she has saved $36, and $36 is 3/4 of the total cost of the game. We can tackle the fraction provided first (3/4). If we change the phrase to a percentage instead of a fraction, 3/4 is the same as 75%. (We get this by dividing 3 by 4, which gives us the decimal 0.75, and to convert this to a percentage, we multiply this by 100). Which is also equal to the fraction 0.75. So, 3/4 = 75% = 0.75.

We also have the information that $36 is equal to 3/4 of the total cost, which means that it is 75% of the total cost, which means that it is 0.75 times the total cost.

One way to get this problem answered is to do "CMAD", which means cross multiple and divide. This principle compares two fraction numbers as equal to one another, and then you cross multiply and divide the fractions. So it would be stated that 3/4 = $36/x, because we don't know the total cost of the game. So if we cross multiply the numbers we do know, we would multiple 36 x 4, because they are diagonal from one another. Then divide that total by the third number we know, which is 3. So, 36 x 4 = 144. Then 144 ÷ 3 = 48. That means that the total cost of the game is $48. We can verify our answer by wondering...what is 75% of the total ($48)? We can figure this out by multiplying $48 x 0.75 (which is the same as 3/4). So 48 x 0.75 = $36!

Another way we can tackle this problem is by multiplying the fraction to figure it out. Going this way, we would say $36 is 3/4 of what number? 36 = 3/4 * X. So we have to get 3/4 to the other side of the equation, and since it is being multiplied on the right side to X, we need to divide it on the other side. So, it would read 36 ÷ 3/4 = X. In order to properly divide the fractions and understand the equation, we should turn the whole number, 36, into a fraction. Any whole number, when represented as a fraction, should be over a 1. (Think about it...if you treat the fraction as a division problem, 36 ÷ 1 = 36). So the final equation we need to solve would be 36/1 ÷ 3/4 = x. When we divide fractions, we need to FLIP the second fraction in our equation. Which would make it 36/1 x 4/3 = x. When multiplying fractions, you multiply across the top and bottom (numerators and denominators). So we get (36 x 4) / (1 x 3) = x. When we do this multiplication, this gives us 144 / 3 = x. Which means that x = 48. To re-state that in the language of the original question, the total cost of the game is $48.

So that gives you two different ways to reach the same outcome, depending on what principles you are learning with this question.

I am happy to answer any other questions you may have. I hope this helps!

Answer 2

Let's create an equation based on what was given to us in the problem. Remember that some key words should translate to specific math symbols. "is" should translate to "=" and "three-fourths of" should translate to "3/4 *". So we have:

36 = 3/4 * total_cost

Can you figure out the rest from here?