Question

Understanding Mathematics, Resource 2, Chapter Nine.

6. If I think of a number, halve it, take away 5 and then add on 3 times the
number I thought of I end up with a number that is 4 more than twice the
number I first thought of. What was the number I first thought of?

7. I think of a number and add it to twice itself. If I then take away one less
than the number first thought of I end up with an answer of 9. Find the
number first thought of.

8 I think of a number, add 4 and then multiply the answer by 5. I could
have achieved the same final answer had I instead multiplied my chosen
number by 4 and then added 5. What was the number I thought of?

9. If I take a particular number from 3, double the answer and take the
result of doing this from the answer obtained by multiplying the particular
number by 3 and adding 15, I end up with 25. What is the particular
number I started with?

10. I think of a number, add three, divide the answer by 2 and then add 7
This gives an answer that is the same as I would have obtained had I
instead doubled the number first thought of and then taken away 8. Find
the number first thought of

Pls answer whichever you can do!

Answer 1

6. 6 is the number I thought of

8. -15 is the number I thought of

Explanation:

6. Let x represent the number you thought of.

x/2 . . . halve it

x/2 -5 . . . take away 5 (from the previous result)

x/2 -5 +3x . . . then add on 3 times the number I thought of

= . . . I end up with ...

4 + . . . four more than ...

4 + 2x . . . ... twice the number I first thought of.

So, the equation is ...

x/2 -5 +3x = 4 +2x

Subtracting 2x we have

x/2 -5 +3x -2x = 4

Adding 5 and collecting terms, we get

(3/2)x = 9

Multiplying by the inverse of the coefficient of x, we get ...

x = (2/3)(9)

x = 6

The number I first thought of was 6.

__

Check

After I halve it, take away 5 and add back 3 times 6, I have ...

3 -5 +18 = 16

After I add 4 to twice the number, I have ...

4 +2·6 = 16

So, the first set of manipulations gives the same result as the second. 6 is the answer.

_____

8. Let x represent the number I thought of.

x +4 . . . add 4

5(x +4) . . . multiply the answer by 5

= . . . . I could get the same final answer by ...

4x . . . multiplying my number by 4

4x +5 . . . then adding 5

So, the equation is ...

5(x +4) = 4x +5

5x +20 = 4x +5 . . . . eliminate parentheses

x + 20 = 5 . . . . . . . . subtract 4x

x = -15 . . . . . . . . . . . subtract 20

The number I thought of was -15.

__

Check

Add 4 and multiply the result by 5: 5(-15+4) = 5(-11) = -55.

Multiply the result by 4 and add 5: 4(-15)+5 = -60+5 = -55, the same final answer.

The answer of -15 checks with the problem statement.