MATH SOLVE

2 months ago

Q:
# 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+1000Account B: y≥1.08x+1000What is true in the context of the situation based on the system of inequalities?Select True or False for each statement.Statement True FalseSally 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.

Accepted Solution

A:

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 + bWhere,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.