The amount of money in Harold's savings account is inversely proportional to the number of bills he has to pay each month. If x represents the number of bills he has to pay each month, and y represents the money in his savings account, find the following: A- use the equation y = k/x to find k, the constant of variation; if Harold has $209 in his bank account when he has 3 bills to pay. B- if Harold has 5 bills to pay this month, how much money will he have in savings? C- If Harold's wife Sylvia sees only $69.67 in their savings account, about how many bills can she assume they had to pay this month?

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Ashraf82 Ashraf82 · Answer 1 · 2019-04-27T07:27:35+02:00

Answer:

Part A: k = 627

Part B: He will have $125.4 in savings

Part C: The number of bills this month he had to pay is 9

Step-by-step explanation:

* Lets study the problem

-The amount of money savings is inversely proportional to the

number of bills should to pay each month

- The number of bills he has to pay each month = x

- The money is saving = y

∵ y ∝ 1/x

∴ y = k/x ⇒ k, is the constant of variation

Part A:

* Harold has $209 in his bank account when he has 3 bills to pay

∵ x = 3 and y= 209 ⇒ substitute these value in the equation of variation

∴ 209 = k/3 ⇒ multiply each side by 3

∴ k = 627

* The equation of variation is ⇒ y = 627/x

Part B:

* Harold has 5 bills to pay this month

∵ x = 5

∴ y = 627/5 = $125.4

* He will have $125.4 in savings

Part C:

* He has $69.67 in his savings account

∵ y = 69.67

∴ 69.67 = 627/x ⇒ use cross-multiplication

∴ 69.67x = 627 ⇒ divide both sides by 69.67

∴ x ≅ 9

* The number of bills this month he had to pay is 9