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An amount of ₹ 5000 is put into three investments at 6%, 7% and 8% per annum respectively. The total annual income from these investments is ₹358. If the total annual income from first two investments is ₹70more
than the income from the third, find the amount of each investment by the matrix method.
HINT: Let these investments be ₹x, ₹y and ₹z, respectively.
Then, x + y + z = 5000, …(i)
6x + 7y + 8z = 35800 …(ii)
6x + 7y - 8z = 7000. …(iii)
Two schools A and B want to award their selected students on the values of sincerity, truthfulness and helpfulness. The school A wants to award ₹ x each, ₹ y each and ₹ z each for the three respective values to 3, 2 and 1 students respectively with total award money of ₹ 1,600. School B wants to spend ₹ 2,300 to award its 4, 1 and 3 students on the respective values (by giving the same award money to the three values as before). If the total amount of award for one prize on each value is ₹ 900, using matrices, find the award money for each value. Apart from these three values, suggest one more value which should be considered for award.
HINT: By the given data, we have