Last year Emily invested some money and had gained 8% profit and her friend, Samira invested some money and gained 9% profit. Their total profit on the two investments was $1720. This year they each decided to invest the same amount of money as last year. Emily gained 7% profit this year and Samira gained 6%. If they receive a total profit of $1280, how much money did Emily invest? Answer.

Emily's investment = $8,000

Step-by-step explanation:

Let Emily's invested amount = x

Let Samira's amount = y

8% of Emily's amount = 8/100 × x = 0.08x

9% of Samira's amount = 9/100 of y = 0.09y

∴ 0.08x + 0.09y = 1720

multiplying through by 100

8x + 9y = 172000 - - - - - (1)

7% of Emily's amount = 0.07x

6% 0f Samira's amount = 0.06y

0.07x + 0.06x = 1280

multiplying through by 100

7x + 6y = 128000 - - - - - - (2)

Next, let us subtract eqn 2 from eqn 1

equation (1) - equation 2

    8x + 9y = 172000

-

    7x + 6y = 128000

=     x + 3y = 44000 - - - - (3)

from eqn (3) x = 44000 - 3y - - - - - (4)

putting this value of x into eqn 1

8x + 9y = 172000

8 (44000 - 3y) + 9y = 172000

352000 - 24y + 9y = 172000

-15y = 172000 - 352000 = -180000

y = 180000 ÷ 15

y = $12,000

finding x using eqn (4)

x = 44000 - 3y

x = 44000 - 3(12000)

x = 44000 - 36000

x = $8,000

∴ Emily's investment = $8,000