## ms.smith invested 25000 in two accounts one yielding 4% interest the other 12%.If she received a total of 2280 in interest at the end of the

Question

ms.smith invested 25000 in two accounts one yielding 4% interest the other 12%.If she received a total of 2280 in interest at the end of the year how much did she invest in each account?

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4 weeks 2021-09-22T14:20:29+00:00 1 Answer 0

1. Answer: Ms Smith invested \$9,000 in one account and \$16,000 in the second account

Step-by-step explanation:

Now let us denote the amount she invested in the first account by “a” and denote the amount she invested in the second account by “b”.

If she invested \$25,000 in the 2 accounts, then:

a + b = \$25000 ——- call this equation (eqn)1

Again, the first account yielded extra 4% of what was invested.

Therefore 4/100 × a = 4a/100 (this is the amount the first account yielded)

The second account yielded extra 12% of the invested amount

Therefore 12%×b = 12b/100

If the total sum of the interest the 2 accounts yielded was 2280, then:

( 4a/100) + (12b/100) = 2280 —–let this be eqn 2

We now have simultaneous equations before us.

In eqn 1, making b the subject of the formula:

b = \$25000 – a

Substitute b for \$25000 – a in eqn 2

(4a/100) + [12(25000 – a)/100] = 2280

300000 – 8a = 228000

– 8a = 228000 – 300000

a = -72000/-8

a = \$9000

Now, we substitute “a” for \$9,000 in eqn 1

9000 + b = 25000

b = 25000 – 9000

b = \$16,000

So, Ms Smith invested separate sums of \$9,000 and \$16000 in the two accounts