Henry and Sean have the same amount of income. If Henry spends $43 a day and Sean spends $14 a day, Sean will have $319 when Henry uses up all his income. If Henry spends $13 a day and Sean spends $43 a day, how much income will Henry have left when Sean uses up all his income?
if they each start with x, we have
x-14d = x-43d + 319
d = 11
so they each started with $473
473 - 11*13 = $330
Let x be the amount of income each have.
Let y be the number of days when Henry used up all his income
Then, we have,
x - 14y = 319 - (1)
and
x - 43y = 0 - (2)
Solving these two
y = 11
=> x = 473
income = $473
number of days = 11
Now when Henry spends $13 & Sean spends $43. Let z be the number of days when Sean uses up all his income.
=> 473 - 43z = 0
z = 11
Thus 473 - 13 * 11 = 330
Hence, Henry will have $330 when Sean uses up all his income
To solve this problem, we can set up two equations based on the given information:
Let's denote the income of Henry and Sean as 'x'.
From the first scenario, we know that when Henry spends $43 a day and Sean spends $14 a day, Sean will have $319 left when Henry uses up all his income. This can be expressed as:
43x = x - 319
Simplifying this equation, we have:
43x - x = -319
42x = -319
Now, let's solve for 'x':
x = -319 / 42
x ≈ -7.60
We find that both Henry and Sean have approximately -$7.60 as their income, which is not possible. It indicates that the given information in the first scenario must be incorrect.
Therefore, we cannot proceed with the given information to find out how much income Henry will have left when Sean uses up all his income.