Four students go shopping at Vaughan Mills. Each student brought a different amount of money to the mall. Chloe brought 5 more than half the amount that Luca brought. Nico brought 2 less than double the amount that Chloe brought. Olivia brought 2 times the amount that Luca brought. Together, all four students brought a total of 778 dollars to the mall. How múch money did each student bring to the mall?
Let's assign variables to represent the amounts of money each student brought:
Let C = amount Chloe brought
Let L = amount Luca brought
Let N = amount Nico brought
Let O = amount Olivia brought
From the information given, we can set up the following equations:
1. C = 5 + (1/2)L
2. N = 2(C)
3. O = 2L
4. C + L + N + O = 778
Substitute equations 1, 2, and 3 into equation 4:
(5 + 1/2L) + L + 2(5 + 1/2L) + 2L = 778
5 + 1/2L + L + 10 + L + 2L = 778
6.5L + 15 = 778
6.5L = 763
L = 117.38
Now, plug L back into the equations to find the amounts for the other students:
C = 5 + 1/2(117.38) = 70.69
N = 2(70.69) = 141.38
O = 2(117.38) = 234.76
Therefore, Chloe brought $70.69, Luca brought $117.38, Nico brought $141.38, and Olivia brought $234.76 to the mall.