Exercise 10 Page 161

Practice makes perfect

a Let B be the amount of money in our account, which currently is $3000

B=3000

We use this only for paying rent, which costs $625 per month. We can write the money in our account after m months as a linear function. B=3000-625m When our balance drops below $700, we get a text alert. When the balance is greater than or equal to this amount, we pay our rent without receiving the text. We can model this using an inequality. 3000-625m ≥ 700

b To find the maximum number of months that we can pay our rent without receiving a text alert, we will solve the inequality from Part A.

3000-625m ≥ 700

SubIneq

LHS-3000≥RHS-3000

-625m ≥ -2300

DivNegIneq

Divide by -625 and flip inequality sign

m≤ 3.68

The maximum number of months we can pay our rent without receiving a text alert is 3. From the solution set, we know that after 3 months we still have enough money in the account not to trigger the text message. It is not until after the 4th month's payment that the balance dips below $700. First month: 3000-625&=2375 Second month: 2375-625&=1750 Third month: 1750-625&=1125 Fourth month: 1125-625&= 500

c From the previous part we know that the maximum number of months we can pay our rent is 3, so the first month is June. We can pay the rent for 2 additional months, which are July and August. After that we will need to make a deposit.

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Exercise 10 Page 161

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