Q:

# 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?

Accepted Solution

A:
Answer:Part A: k = 627Part B: He will have $125.4 in savingsPart C: The number of bills this month he had to pay is 9Step-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 variationPart 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/xPart B:* Harold has 5 bills to pay this month∵ x = 5∴ y = 627/5 = $125.4* He will have$125.4 in savingsPart 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