Can someone help me with this...
Mr and Mrs Lim went shopping with a total of $712.50. After buying some items each, the amount Mrs Lim had left was 4 times the amount she spent and the amount Mr Lim had left was trice the amount he spent. Both of them had a total of $555 left, how much did each of them have at first?
Try setting up the algebraic equations and solving them. Let the starting amounts be x for Mr Lim and y for Mrs Lim.
x + y = 712.50
1/5 of x was spent
1/3 of y was spent
(4/5) x + (2/3) y = 555
Solve the two equations in two unknowns.
To solve this problem, let's break it down step by step.
Let:
- x be the amount Mrs. Lim spent
- y be the amount Mr. Lim spent
We are given the following information:
1. "After buying some items each, the amount Mrs. Lim had left was 4 times the amount she spent."
This means that Mrs. Lim had 4x dollars left.
2. "The amount Mr. Lim had left was three times the amount he spent."
This means that Mr. Lim had 3y dollars left.
3. "Both of them had a total of $555 left."
This means that the sum of Mrs. Lim's and Mr. Lim's remaining amounts is $555:
4x + 3y = $555 (equation 1)
4. "Mr and Mrs Lim went shopping with a total of $712.50."
The total amount spent by both of them is $712.50, which can be expressed as:
x + y = $712.50 (equation 2)
We now have a system of two equations with two unknowns. We can solve this system of equations to find the values of x and y.
Using equation 2, we can express x in terms of y:
x = $712.50 - y
Substituting this expression into equation 1:
4($712.50 - y) + 3y = $555
Expanding and simplifying:
2850 - 4y + 3y = $555
2850 - y = $555
- y = $555 - $2850
- y = -$2295
y = $2295 (Mr. Lim's spent amount)
Substituting this value back into equation 2 to find x:
x + $2295 = $712.50
x = $712.50 - $2295
x = -$1582.50
It seems that we have obtained negative values for x and y, which doesn't make sense in the context of the problem. This suggests that there might be a mistake in the problem statement or its data.