Answer:
The general form of the equation is;
25·x + 12·y = 75,000
x + y ≤ 6,250
When they work the same duration, the time the husband and wife works is approximately 2,071 hours each
When they contribute the same amount, the wife, works for x = 1,500 hours, while the husband works for y = 3,125 hours
Explanation:
The amount the couple intends to save in 13 years = $75,000
The amount the wife makes per hour = $25
The amount the husband makes per hour = $12
The number of working hours in 13 years is given as follows;
Total number of hours = 40 hr/week × 52 weeks/year × 13 years = 27,040 hours
However, when the husband alone works, we have;
75,000/12 = 6,250 hours
Let 'x' and 'y' represent the number of hours the wife and husband works respectively, we have the following system of equations;
The general form of the equation is;
25·x + 12·y = 75,000
x + y ≤ 6,250
When the couple work equal times
25·x + 12·y = 75,000...(1)
x = y...(2)
From equation (1), we have;
25·x + 12·y = 75,000
25·x + 12·x = 75,000
x = 75,000/37 ≈ 2,071 hours = y
The number of hours each will work is approximately 2,071 hours
When the husband and wife contribute the same amount, we have;
25·x = 12·y = 75,000/2
x = 75,000/(2 × 25) = 1,500
∴ x = 1,500 hours
The number of hours the wife works = 1,500 hours
y = 75,000/(2 × 12) = 3,125
∴ y = 3,125 hours
The number of hors the husband works = 3,125 hours