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? use let statement
Let's use variables to represent the amount of money each student brought to the mall.
Let:
- Chloe's amount be C
- Luca's amount be L
- Nico's amount be N
- Olivia's amount be O
According to the given information:
1. C = (L/2) + 5
2. N = 2C - 2
3. O = 2L
4. C + L + N + O = 778
Now we can substitute the expressions for C, N, and O into the equation for the total amount of money brought to the mall:
(L/2 + 5) + L + (2(L/2 + 5) - 2) + 2L = 778
Simplify the equation:
(L/2 + 5) + L + (L + 10) - 2 + 2L = 778
L/2 + 5 + L + L + 10 + 2L - 2 = 778
2.5L + 13 = 778
2.5L = 765
L = 306
Now that we have found Luca's amount, we can find the amounts for the other students:
- Chloe: C = (306/2) + 5 = 153 + 5 = 158
- Nico: N = 2(158) - 2 = 316 - 2 = 314
- Olivia: O = 2(306) = 612
Therefore, Chloe brought $158, Luca brought $306, Nico brought $314, and Olivia brought $612 to the mall.