Carlos is saving money to buy a game. So far he has saved $30 , which is five-sixths of the total cost of the game. How much does the game cost?

2 Answers
Feb 18, 2018

#T=$36#

Explanation:

Hmm...

Let's organize this problem.

Since he saved #$30#, he as #$30#

Now, that is five-sixths of the total cost of the game.

Let's name the total cost #T#.

If we have a fraction of something, say, half of four, we multiply the fraction by the whole.

#"half of four"#
#1/2*4#

Similarly, five-sixths of the total can be represented as:

#5/6*T#

Now, the problem is telling us that #$30# is equal to the expression above.

Therefore, #5/6*T=30#

=>#6/5*5/6*T=6/5*30/1#

=>#1*T=6/cancel5*cancel30/1#

=>#T=$36#

Feb 18, 2018

#$36=T#

Explanation:

Here is a little trick:

For many algebra problems,

is#=# equal sign
of#=#multiplication.

I put parenthesis around the key words.

#"Carlos is saving money to buy a game. So far he has saved $30, "##"which (is) five-sixths (of) the total cost of the game. How much "##"does the game cost?"#

Really, the second sentence is what matters for us. We replace the key words with mathematical signs.

#"So far he has saved $30, which =5/6*total cost of the game."#

Now that looks like an equation!

The equation is:

#30=5/6*T# Where #T# is the total cost.

We now solve the equation.

=>#30/1=(5T)/6# cross multiply.

=>#180=5T#

=>#180/5=(cancel5T)/cancel5#

=>#$36=T#