Salina’s age is one-quarter the age of her aunt. If a represents her aunt’s age, which expression represents Salina’s age?
1 answer:
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Answer:
a = 3
b = 4
Step-by-step explanation:
Simultaneous equation
3a = 2b + 1
3a - 2b = 1 ------------------(I)
3b = 5a - 3
-5a + 3b = -3 --------------(II)
Multiply equation (I) by 3 & equation (II) by 2 and then add. So, now 'b' will be eliminated and we can find the value of 'a'.
(I)*3 9a - 6b = 3
(II)*2 <u>-10a + 6b = -6</u> {Now add}
-a = -3
a = -3/(-1)
Plugin a = 3 in equation (I)
3*3 - 2b = 1
9 - 2b = 1
-2b = 1 - 9 {Subtracting 9 from both sides}
-2b = - 8
b = (-8)/(-2) {Dividing both sides by (-2_}
Answer:
18. compound interest
19. simple interest
20. simple interest
Step-by-step explanation:
For these problems, the initial balance is irrelevant. All that matters is the multiplier of that balance. For simple interest at rate r for t years, the multiplier is ...
simple interest multiplier = (1 +rt)
For interest compounded annually, the multiplier of the initial balance is ...
compound interest multiplier = (1 +r)^t
A spreadsheet can do the computations for you.
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As an example of the computations involved, consider problem 19:
simple interest multiplier = 1 + 0.13·6 = 1.78
compound interest multiplier = 1.10^6 = 1.771561
The latter is less than the former, so the simple interest account will have the (slightly) greater balance at the end of 6 years.
