Question

HREE 8. I invest £x at 3% per annum and £y at 4% per annum. My annual income from these investments is £22. Had I invested £y at 3% and £x at 4%, my income would have been £20 per annum. Find x.​

Answer 1

Answer:

x = £200

(y = £400)

Step-by-step explanation:

Convert interest rates into decimal format:

3% = 3/100 = 0.03

4% = 4/100 = 0.04

From information given, create 2 equations:

0.03x + 0.04y = 22

0.04x + 0.03y = 20

Rearrange equation 1 to make y the subject:

⇒ 0.03x + 0.04y = 22

⇒ 0.04y = 22 - 0.03x

⇒ y = 550 - 0.75x

Substitute y = 550 - 0.75x into equation 2 and solve for x:

⇒ 0.04x + 0.03(550 - 0.75x) = 20

⇒ 0.04x + 16.5 - 0.0225x = 20

⇒ 0.0175x = 3.5

⇒ x = 200

To find y, substitute found value of x into one of the equations and solve for y:

⇒ 0.04(200) + 0.03y = 20

⇒ 8 + 0.03y = 20

⇒ 0.03y = 12

⇒ y = 400