and
Simplify the following:
a) 2a x 3g
b) - 6b x d
c) 2(x+3) + 4x
d) 3(ad - 4a) + 8(a - 2d)
Sorry about this guys, you'll probably find it pretty easy so you can help me.
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
Start each of these question by representing the question with an equation.
a)Half of the number means: and adding 9 to it gives us:When he adds nine to half of the number...
So the previous part is equal to 54:the result is 54.
Now simply solve by subtracting 9 from both sides, then multiplying both sides by 2.
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b)We have that 5 is being subtracted from a number:If five is taken from a number...
So we double the previous part:the result is doubled...
So our expression is equal to 6:the answer is six.
Now, simply solve for n by dividing both sides by 2, and then adding 5 to both sides.
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c)This means adding 5 to a number:Five more than a number...
This implies an equals operator:is equal to...
This means that we subtract 1 from our number, then multiply the result by 3:three times one less than the number.
Multiply both sides by 3, add 1 to both sides to get:
Then subtract from both sides to get:
Multiply both sides by 3 then divide by 2 to get your final answer.
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.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?
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?
Hello,
Let n be the number he was thinking of.
The tip is to start from "the number" in the sentence and to take the words one by one before it :a) George is thinking of a number. When he adds nine to half of the number, the result is 54.
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