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Simple Math Help!

Chiclet

TRIBE Promoter
Hi guys, I'm doing a sample test (Liberal Arts and Sciences Test) to hopefully help me with getting into/completing elementary Teacher's college.

I am SO bad at math and I am stuck on these questions (and it's only level 1... God.)

Can someone please tell me how to answer these questions?

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?
2 hours and 24 minutes
3 hours and 12 minutes
3 hours and 44 minutes
4 hours and 10 minutes
4 hours and 33 minutes


If 300 jellybeans cost you x dollars. How many jellybeans can you purchase for 50 cents at the same rate?
150/x
150x
6x
x/6
1500x

And tell me step by step how you solved it?

Thank you thank you! There may be more to come! I can't believe I ever got through High School math in one piece.
 

Dr Funk MD

TRIBE Promoter
Chiclet said:
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?
Chances are Sally and Jack will argue over who's doing the better job and who's turn it is to get more paint. It will take two days.

The make up sex will take 20 minutes.
 

Eclectic

TRIBE Member
If Sally can paint the house in 4 hours and John in 6, to get halfway done Sally needs 2 hours, John needs 3. That means in 2 hours Sally is half done while John is 1/3 done.

In 2 hours 5/6 of the house will be painted.
Sally can paint 1/8 in 30 minutes while it will take John appoximately 45 minutes.
The remaining 1/6 will take them 24 minutes to paint together.

I hope that makes sense. It's hard to describe how my brain works.
 

stanimal

TRIBE Member
Chiclet said:
If 300 jellybeans cost you x dollars. How many jellybeans can you purchase for 50 cents at the same rate?
150/x
150x
6x
x/6
1500x

And tell me step by step how you solved it?

Thank you thank you! There may be more to come! I can't believe I ever got through High School math in one piece.
Well, we're given this:

300 jellybeans * cost per jellybean = x dollars

We can rearrange this equation to:

cost per jellybean = x dollars / 300 jellybeans


And we want to find y, where y is the # of jellybeans we can purchase:

y jellybeans * cost per jellybean = 0.50 dollars

Rearrange as above:

cost per jellybean = 0.50 / y


Since we're told that the cost (or rate) is the same, we can equate the two:

x / 300 = 0.50 / y

Solve for y.

y = 150 / x
 

Chiclet

TRIBE Promoter
Eclectic said:
If Sally can paint the house in 4 hours and John in 6, to get halfway done Sally needs 2 hours, John needs 3. That means in 2 hours Sally is half done while John is 1/3 done.

In 2 hours 5/6 of the house will be painted.
Sally can paint 1/8 in 30 minutes while it will take John appoximately 45 minutes.
The remaining 1/6 will take them 24 minutes to paint together.

I hope that makes sense. It's hard to describe how my brain works.
Um... I kind of get it, but could you put it in an equation for me please? :D

Thank you thank you! If not, I think I can evenutally understand it...
 
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s1k

TRIBE Member
usually it's best to solve these problems by developing a formula.

so if 1 takes 4 hours to do a house, and one takes 6 hours..their speed is 1/4 and 1/6 house per hour. If you convert these to percentages (another form of fractions) you get 0.25 (1/4) and 0.166 (1/6)...now you know you are trying to complete 1 house sooo...

let x be the number of hours spent on painting....

0.25x+0.166x=1 so now just solve for x=2.4 so 2 hours and 4/10 of an hours...60 minutes times 0.4 gives 24. so the answer is 2:24
 

Chiclet

TRIBE Promoter
stanimal said:
Well, we're given this:

300 jellybeans * cost per jellybean = x dollars

We can rearrange this equation to:

cost per jellybean = x dollars / 300 jellybeans


And we want to find y, where y is the # of jellybeans we can purchase:

y jellybeans * cost per jellybean = 0.50 dollars

Rearrange as above:

cost per jellybean = 0.50 / y


Since we're told that the cost (or rate) is the same, we can equate the two:

x / 300 = 0.50 / y

Solve for y.

y = 150 / x

Thank you!
 
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s1k

TRIBE Member
^^ i think you factor out x and isolate...then x equals 6...then sub in and it equals 33. i could be wrong though...see if final answer is 33.
 

stanimal

TRIBE Member
Chiclet said:
OK, here's another:

If 8x + 5x + 2x + 4x = 114, then 5x + 3 =
12
25
33
47
86
Ok, all these problems are essentially the same. The key, as someone mentioned above, is coming up with the correct equation(s) and solving for the variables. Don't get intimidated by the x's and y's. Just think of them as apples or oranges if you must.

So for this question, you're actually given the equations.

8x + 5x + 2x + 4x = 114

This is the same as 19x = 114 or simply x = 6.

Well in that case 5x + 3 = 5(6) + 3 = 33


First step in these type of problems is determining the correct equations (usually only 2 in your case). And relate them to each other somehow and solve for the missing variable.
 

coleridge

TRIBE Member
Chiclet said:
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?
2 hours and 24 minutes
3 hours and 12 minutes
3 hours and 44 minutes
4 hours and 10 minutes
4 hours and 33 minutes
There are two ways to approach this.

The first (and the way they'd want to see if you have to write out your steps).

This is a rate question. So if SR = Sally's Rate of Painting (in houses per hour), JR = John's Rate of Painting (in houses per hour), t = the time they spend painting, and n = number of houses completed in that time:

The formula for this problem would be:

(SR x t) + (JR x t) = n

(Sally's Rate of Painting x Time Painting) + (John's Rate of Painting x Time Painting) = Number of Houses Painted

Now we know:

SR = 1/4 house per hour
JR = 1/6 house per hour
n = 1 hour

so (1/4 x t) + (1/6 x t) = 1

solve for t:

t/4 + t/6 = 1
6t/24 + 4t/24) = 1
10t/24 = 1
t=24/10
t=2.4 hours

or 2 hours 24 minutes.

or...............

You could approach this question by working backwards from the answers. Pick an answer and figuring out how many houses will be painted in that time:

For example I'd pick the middle answer and work from there:

so in 3 hours and 44 minutes

Sally paints one house in 4 hours (240 minutes)

so in 3 hours and 44 minutes (224 minutes) Sally will paint 0.93 houses.

John paints one house in 6 hours (360 minutes)

so in 3 hours and 44 minutes (224 minutes) John will paint 0.62 houses.

Add the two together and it would be 1.56 houses.

Too high, so you'd move to a smaller number and try again.
 
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