Question

Sally invested money into two different accounts at the same time. The system of inequalities represents the balance of each account where x represents the number of years the money has been invested.
Account A: y≥1.13x+1000


Account B: y≥1.08x+1000




What is true in the context of the situation based on the system of inequalities?


Select True or False for each statement.


Statement True False

Sally initially invests more money into Account A than Account B.


The rate at which the balance of Account A grows is greater than the rate at which the balance of Account B grows.


Sally invests a total of $1000 into the two accounts.

Answer 1

Answer: The true statement is,

The rate at which the balance of Account A grows is greater than the rate at which the balance of Account B grows.

Step-by-step explanation:

Given inequalities that represents the amount in two different account,

Account A: y ≥ 1.13x+1000,

Account B: y ≥ 1.08x+1000,

Since, the amount of an investment represents by the linear equation,

y = ax + b

Where,

b = invested amount,

a = amount of interest per period,

x = number of periods,

Since, related equation of inequality y ≥ 1.13x+1000,

y = 1.13x+1000,

i.e invested amount = 1000, interest per year = 1.13,

Similarly, related equation of inequality y≥1.08x+1000,

y = 1.08x+1000,

i.e invested amount = 1000, interest per year = 1.08,

⇒ Sally initially invests same money into Account A than Account B

⇒ Sally invests a total of $2000 into the two accounts.

Now, 1.08 < 1.13

∵ interest ∝ rate × time,

Hence, the rate at which the balance of Account A grows is greater than the rate at which the balance of Account B grows.