Mdm Lee gave Nathan and Jasper some money on Friday.On Saturday,Nathan gave 1/3 of the amount he had to Jasper.On Sunday,Jasper gave 1/3 of the amount he had to Nathan.In the end,Nathan had $96 and Jasper had $120.How much did each of them have at first?
Friday: the amounts are
n and j
Saturday:
2n/3 and j+n/3
Sunday:
2n/3 + (1/3)(j+n/3) and (2/3)(j+n/3)
= j/3 + 7n/9 and 2j/3 + 2n/9
so,
j/3 + 7n/9 = 96
2j/3 + 2n/9 = 120
Nathan had $54 and Jasper had $162
I'll let you verify the accuracy of the solution.
I still don't really understand though due to the /
To solve this problem, we can use algebraic equations. Let's represent the amount Mdm Lee gave to Nathan as "x" and the amount she gave to Jasper as "y".
On Saturday, Nathan gave 1/3 of the amount he had to Jasper. Therefore, Nathan had 2/3 left of the amount he originally had, which is (2/3) * x.
On Sunday, Jasper gave 1/3 of the amount he had to Nathan. Therefore, Jasper had 2/3 left of the amount he originally had, which is (2/3) * y.
From the given information, we can set up two equations:
(2/3) * x = 96 -- equation 1
(2/3) * y = 120 -- equation 2
To solve for the values of x and y, we'll multiply both sides of equation 1 by 3/2 and equation 2 by 3/2:
(3/2) * (2/3) * x = (3/2) * 96
x = (3/2) * 96
x = 144
(3/2) * (2/3) * y = (3/2) * 120
y = (3/2) * 120
y = 180
Therefore, Nathan originally had $144, and Jasper originally had $180.