Final answer:
Cheko received $250 at the start of last week. This was calculated by solving the equation formed from the ratio of their initial pocket money (3:5) and the total amount they had after receiving an additional $35 each, which summed up to $470.
Step-by-step explanation:
To find out how much money Cheko received at the start of last week, we need to use the given ratio and the total amount of money they ended up with after receiving an additional $35 each. The initial ratio between Miko and Cheko's pocket money is 3:5. Let's assign the variable x to represent the common factor for their initial amounts. Therefore, Miko had 3x dollars and Cheko had 5x dollars initially.
At the end of the week, both received an additional $35. The total money they have is then 3x + 35 for Miko and 5x + 35 for Cheko. The sum of their money is $470 as given in the problem. By setting up the equation (3x + 35) + (5x + 35) = 470, we can solve for x:
- 3x + 5x + 35 + 35 = 470
- 8x + 70 = 470
- 8x = 470 - 70
- 8x = 400
- x = 50
Now that we have the value for x, we can find out how much Cheko received initially:
Cheko's initial amount = 5x
= 5(50)
= $250
Therefore, Cheko received $250 at the start of last week.