Question

On two investments totaling $7,500, Lydia lost 2% on one and earned 5% on the other. If her net annual receipts were $158, how much was each investment

Answer 1

Lydia invested $ 3100 in investment lost 2 % and invested $ 4400 in investment that earned 5 %

Solution:

Given that on two investment totaling $ 7500

Lydia lost 2% on one and earned 5% on the other

Her net annual receipts were $158

To find: amount invested in both investments

Let Lydia invest $ x in first investment where she lost 2 %

Let Lydia invest $ y in second investment where she earned 5 %

Total investment given = 7500

x + y = 7500 ---- eqn 1

Net annual receipt = 158

5 % y- 2 % x = 158

$\frac{5}{100}y - \frac{2}{100}x = 158$

0.05y - 0.02x = 158 ------- eqn 2

Let us solve eqn 1 and eqn 2

From eqn 1,

x = 7500 - y

Substitute x = 7500 - y in eqn 2

0.05y - 0.02(7500-y) = 158

0.05y -150 + 0.02y = 158

0.07y = 158 + 150

0.07y = 308

y = 4400

Thus,

x = 7500 - y

x = 7500 - 4400

x = 3100

Thus she invested $ 3100 in investment lost 2 % and invested $ 4400 in investment that earned 5 %