### Instruction: Amanda, Ben, and Carlos share a sum of money. Their portions are in the ratio of 1:2:7, respectively. If Amanda's portion is $\$$20, what is the total amount of money shared?### Response: To solve this problem, I need to find the value of the whole sum of money, which I will call S.
I know that Amanda's portion is 1/10 of the whole sum, since 1 is one-tenth of 1 + 2 + 7, which is the sum of the ratio numbers.
So I can write an equation: 1/10 * S = 20, where 20 is Amanda's portion.
To solve for S, I need to multiply both sides of the equation by 10.
This gives me: S = 20 * 10, which simplifies to S = 200.
Therefore, the total amount of money shared is $\$$200.