Project Maths Algebra Questions

dtfo

Hi Im having trouble with a few questions from the active maths 4 book for higher level, page 64 Q4 and 65 Q10 if anyone could help

Q4 - Catherine has €3,000 to invest. She invests a sum of money at 9% per annum and the rest at 5% per annum. If the return on the higher interest rate is €95 more than the lower rate, how much did she invest at each rate?

Q10 - When the two digits of a two-digit number are added together, the answer is 12. The two-digit number obtained by swapping the digits around is 18 more than the original number. Find the two digits.

internelligent

Q4

x = sum at 9%
y = sum at 5%

x + y = 3000

9/100x - 5/100 y = 95
=> 9x - 5y = 9500

x + y = 3000
9x - 5y = 9500

Quadratic equations from there

The second one I just use process of elimination since there are so few possibilities. Don't have the energy to write an equation

Skinhead Kane

internelligent wrote: »

Q4

x = sum at 9%
y = sum at 5%

x + y = 3000

9/100x - 5/100 y = 95
=> 9x - 5y = 9500

x + y = 3000
9x - 5y = 9500

Quadratic equations from there

The second one I just use process of elimination since there are so few possibilities. Don't have the energy to write an equation

I was going to write that before you edited.

dtfo

Thanks very much. Just made a silly mistake , I said the return on x = the return on y -€95(instead of +95)

If any one could write up the eqn for Q10 Id really appreciate it as there is another similar question to it Im stuck on

Skinhead Kane

dtfo wrote: »

Thanks very much. Just made a silly mistake , I said the return on x = the return on y -€95(instead of +95)

If any one could write up the eqn for Q10 Id really appreciate it as there is another similar question to it Im stuck on

10x + (12-x) + 18 = 10(12-x) + x

9x + 30 = 120x - 9x

18 x = 90
X = 90/18 = 5
Y = 12 - 5 = 7

CookieMonster.x

You can do the first question another way.
0.09(3000-x) and
0.05x

So 0.09(3000-x) = 0.05x + 95
270-0.09 = 0.05x +95
0.14x=1250
X = 1250

So the amount at 9% was 3000-1250 = 1750 and the amount at 5% was 1250.
If you don't understand it just ask.