Lucky and Ajay are given some money each week. If Lucky and Ajay each spend 40 and 10 respectively in a day, Lucky will still have 700 when Ajay has spent all his money. If Lucky and Ajay each spend 10 and 40 a day, Lucky will still have 1075 when Ajay has spent all his money. How much money is given to Lucky each week?
Don't understand. If Ajay spends 10, then s/he will have no money. How does Ajay get the 40 to spend?
L - 40 d = 700
A - 10 d = 0
multiply second eqn by 4
L - 40 d = 700
4A - 40 d = 0
===========subtract
L - 4 A = 700
L - 10 e = 1075
A - 40 e = 0
multiply first eqn by 4
4 L - 40 e = 4300
A - 40 e = 0
----------------------subtract
4 L - A = 4300
L - 4 A = 700 from above
multiply first one by 4
16 L - 4 A = 17200
L - 4 A = 700
-----------------------------subtract
15 L = 16500
L = 1100
To find out how much money is given to Lucky each week, we need to set up a system of equations based on the given information.
Let's say the amount of money given to Lucky each week is "x" and the amount of money given to Ajay each week is "y".
From the first scenario:
Lucky spends 40 each day, so in a week (7 days), he spends 7 * 40 = 280.
Ajay spends 10 each day, so in a week (7 days), he spends 7 * 10 = 70.
Given that Lucky still has 700 when Ajay has spent all his money, we can write the equation: x - 280 = 700 - y.
From the second scenario:
Lucky spends 10 each day, so in a week (7 days), he spends 7 * 10 = 70.
Ajay spends 40 each day, so in a week (7 days), he spends 7 * 40 = 280.
Given that Lucky still has 1075 when Ajay has spent all his money, we can write the equation: x - 70 = 1075 - y.
Now we have a system of two equations:
Equation 1: x - 280 = 700 - y
Equation 2: x - 70 = 1075 - y
To solve this system of equations, we can use substitution or elimination method.
Let's use the elimination method:
Rearrange Equation 1 to get y in terms of x:
y = x - 280 + 700
Substitute y in Equation 2 with x - 280 + 700:
x - 70 = 1075 - (x - 280 + 700)
Simplify the equation:
x - 70 = 1075 - x + 280 - 700
Combine like terms:
x + x = 1075 + 280 - 70 + 700
Simplify further:
2x = 1985
Divide both sides by 2:
x = 1985/2
Therefore, the amount of money given to Lucky each week is 1985/2 or 992.50.