Question

1) Highland has a population of 12,200. Its population has been increasing at a rate of 300 people per year. Write an equation for the population of Highland.

2) Lowville has a population of 21,000 that is decreasing by 250 people per year. Write an equation for the population of Lowville.

3) Assuming the rates of change do not vary, in how many years will the populations be equal? What will that population be?

Emma and James are spies.

4) Emma opened a savings account with $50. She just got a new spying job and is determined to save $30 a week. Write an equation for Emma's bank account balance.

5) James started a savings account with $75. He also got a new spying job but with a less wealthy country. James will be able to save $25 a week. Write an equation for James's bank account balance.

6) What do your variables represent?

7) Find the solution of the system. What does it represent?

James and Emma both want to buy new bicycles. The bicycles cost $300.

8) How long will it take Emma to save enough money to buy a bike?

9) How long will it take James to save enough money to buy a bike?

James and Emma both had their cover blown and need to go into hiding at the end of six weeks.

10) Do they have enough money so each of them could buy a bike to escape on or will they have to flee on foot?

11) If Emma needs to spend $40 a week to stay in hiding and James needs to spend $35 a week to hide, will there be a time when they both have equal amounts of money left? When would this be and how much will each of them have?

12) Should Emma and James try to escape to hide in Highland or Lowville? Explain your answer.

Answer 1

1.Ans:
Actual formula or equation = 300x +12200 (note: Assume "x" as years)
Highland new population = 300 x (number of years) +12200
example: it's been 2 years
300 x 2 + 12200 = 12800 is the new population

2. Ans:
Actual formula or equation= 21000 - 250x
Lowville new population= 21000 - 250 x (number of years)
example: it's been 4 years
21000 - 250 x 4 = 20000 is the new population

3. Ans: Population is equal after

12200 + 300x = 21000 - 250x

300x + 250x = 21000 - 12200 (note: put number with x on same side)

x = 8800/550

x = 16 years

4. Ans: $50 + ($30 x w) is the equation for Emma's Bank account balance
Let W be number of weeks

5. Ans: $70 + ($25 x w) is the equation for James's Bank account balance

6. Ans: W represents number of weeks
since $50 and $70 is start up money for Emma and James it is there until closing the account.

7. Ans: I do not understand this question im sorry

8. Ans: It will take Emma 9 weeks to save up enough money to buy a bicycles
$50 +($30 x 9) = $320

9.Ans: It will take James 10 weeks to save up enough money to buy a bicycles
$70 +($25x10) = #320

10.Ans: Assuming they have to escape now and not wait 9 or 10 weeks like i said in previous answer then they need to flee on foot.

11. Ans: In 5th week Emma's is left with 0 money and in 7th week James is left with 0 money

12. Ans: They should go to highland if they want to minimize their risk of getting caught.