1. ## Algebraic Equations

I've just got a mental block:

Use Algebraic Equations to solve the following. Let the number be represented by n.

a) George is thinking of a number. When he adds nine to half of the number, the result is 54.
What was the number George was thinking of?
b) If five is taken from a number and then the result is doubled, the answe is six. What was the number?
c) Five more than a number is equal to three times one less than the number. What is the number?

also

A mixture contains peanuts and almonds in the ratio of 5:1. If there is 420 g of the mixture, how many grams of peanuts are in it?

thanks heaps xxx

2. and

Simplify the following:

a) 2a x 3g
b) - 6b x d
c) 2(x+3) + 4x
d) 3(ad - 4a) + 8(a - 2d)

3. Start each of these question by representing the question with an equation.

a)
When he adds nine to half of the number...
Half of the number means: $\displaystyle \frac {1}{2}n$ and adding 9 to it gives us:

$\displaystyle \frac {1}{2}n + 9$

the result is 54.
So the previous part is equal to 54:

$\displaystyle \frac {1}{2}n + 9 = 54$

Now simply solve by subtracting 9 from both sides, then multiplying both sides by 2.

-------------------------------------------------------------------------------------------------------------------------------------------

b)
If five is taken from a number...
We have that 5 is being subtracted from a number:

$\displaystyle n-5$

the result is doubled...
So we double the previous part:

$\displaystyle 2(n-5)$

So our expression is equal to 6:

$\displaystyle 2(n-5) = 6$

Now, simply solve for n by dividing both sides by 2, and then adding 5 to both sides.

-------------------------------------------------------------------------------------------------------------------------------------------

c)
Five more than a number...
This means adding 5 to a number:

$\displaystyle n+5$

is equal to...
This implies an equals operator:

$\displaystyle n+5 =$

three times one less than the number.
This means that we subtract 1 from our number, then multiply the result by 3:

$\displaystyle n+5 = 3(n-1)$

Multiply both sides by 3, add 1 to both sides to get:

$\displaystyle \frac {n}{3}+\frac {8}{3} = n$

Then subtract $\displaystyle \frac {n}{3}$ from both sides to get:

$\displaystyle \frac {8}{3} = \frac {2n}{3}$

Multiply both sides by 3 then divide by 2 to get your final answer.

4. A mixture contains peanuts and almonds in the ratio of 5:1. If there is 420 g of the mixture, how many grams of peanuts are in it?
A ratio of 5:1 means that for every 5 peanuts there is 1 almond, and for every 1 almond, there are 5 peanuts. Another way to say this is that 5 out of every 6 units are peanuts.

So, if we have 420 grams of this mixture, and 5 out of every 6 grams are peanuts, how many grams of peanuts do we have?

Simply multiply 5/6 by 420 to get your final answer of 350 grams.

Any questions?

5. can you tell me the process that you went through to get: the 1/2n + 9...
how did the 54 come out of that? what do i subtract, multiply or whatever you do.
Sorry it's been a long day.

6. Hello,

Let n be the number he was thinking of.

a) George is thinking of a number. When he adds nine to half of the number, the result is 54.
The tip is to start from "the number" in the sentence and to take the words one by one before it :

Half of the number is n/2
He adds nine make it 9+(n/2)
The result is 54, so 9+(n/2)=54

Now, isolate n :
9+(n/2)-9=54-9
n/2=45
2*(n/2)=2*45
n=90

7. Originally Posted by topher0805

c)

This means adding 5 to a number:

$\displaystyle n+5$

This implies an equals operator:

$\displaystyle n+5 =$

This means that we subtract 1 from our number, then multiply the result by 3:

$\displaystyle n+5 = 3(n-1)$

Multiply both sides by 3, add 1 to both sides to get:

$\displaystyle \frac {n}{3}+\frac {8}{3} = n$

Then subtract $\displaystyle \frac {n}{3}$ from both sides to get:

$\displaystyle \frac {8}{3} = \frac {2n}{3}$

Multiply both sides by 3 then divide by 2 to get your final answer.
---------------
I'm lost from here: where did the 3 come from? (n - 1)??
I'm not that good at calculating these fractions, when there is just a pronumeral.
Can you help?