# Thread: Math questions from ACT

1. ## Math questions from ACT

If Sally can paint a house in 4 hours, and John can paint the same house in 6 hour, how long will it take for both of them to paint the house together?

The sales price of a car is $12,590, which is 20% off the original price. What is the original price? I need step by step instructions. 2. Originally Posted by eh501 The sales price of a car is$12,590, which is 20% off the original price. What is the original price?
I need step by step instructions.
$\displaystyle x\times 0.8 = 12,590$

$\displaystyle x = \frac{12,590}{0.8}$

You need to show us some working so we can help you understand how to get the answer.

3. Hello eh501
Originally Posted by eh501
If Sally can paint a house in 4 hours, and John can paint the same house in 6 hour, how long will it take for both of them to paint the house together?
...
I need step by step instructions.
Work out what fraction of the house each one will paint in one hour, and add the two fractions together:

In one hour, Sally paints $\displaystyle \tfrac14$ of the house, and John paints $\displaystyle \tfrac16$. So together they will paint $\displaystyle \tfrac14+\tfrac16 = \tfrac{3+2}{12}=\tfrac{5}{12}$ of the house.

The next question is: How do we then find out how long it will take to paint the whole house? This is the same question as 'How many $\displaystyle \tfrac{5}{12}$'s do we need to make $\displaystyle 1$?' This is a 'divide' question, like 'How many $\displaystyle 3$'s do we need to make $\displaystyle 15$?' The answer to this one is $\displaystyle 15 \div 3=5$. So the answer to the house-painting question is the same: 'How many $\displaystyle \tfrac{5}{12}$'s do we need to make $\displaystyle 1$?' Answer: $\displaystyle 1 \div \tfrac{5}{12}$.

Can you remember how to divide by a fraction? You turn it 'upside-down' and multiply' (Or, to be more technically correct, 'multiply by its reciprocal'.)

So $\displaystyle 1 \div \frac{5}{12}=1\times \frac{12}{5}= \frac{12}{5}= 2.4$

So there's the answer: 2.4 hours, or 2 hours 24 minutes.

4. The sales price of a car is $12,590, which is 20% off the original price. What is the original price? Er i am lazy to use the maths thingy. So, i will just explain it here.$12590 is the price of the car after 20% off
which means $12590 is 80% because everything starts at 100% so 100%-20%=80% so to find 100%, all you need to do is the take$12590 divide by 80
and multiply it by 100

5. Originally Posted by eh501
If Sally can paint a house in 4 hours, and John can paint the same house in 6 hour, how long will it take for both of them to paint the house together?

The sales price of a car is \$12,590, which is 20% off the original price. What is the original price?

I need step by step instructions.
Since the actual test you take will have different exercises, you might want to learn the general methods, rather than trying merely to memorize the steps in the solutions provided for just these examples. If you're interested, try the following:

Google results for "solving percent of word problems"

Google results for "solving work word problems"

These are common and typical sorts of examples, so being familiar with the general methods would probably be wise.