S and O are solving problems. For every three problems that S solves, O solves seven. Together, they solved 180 problems in seven days. How many problems did S solve that week?
Let P be the number of problems S solved and O solved 7/3 * P = (7/3)P problems.
Together they solved P + (7/3)P = 180 problems in 7 days.
Combining like terms, we get (10/3)P = 180.
Dividing both sides by (10/3), we get P = (3/10) * 180 = <<(3/10)*180=54>>54. Answer: \boxed{54}.
Let's start by assigning variables to the unknowns:
Let's say S solved x problems.
Since O solves 7 problems for every 3 problems that S solves, O would solve (7/3)x problems.
Together, in 7 days, they solved 180 problems. So, we can set up the equation:
x + (7/3)x = 180
To solve this equation, we can eliminate the fraction by multiplying both sides by 3:
3x + 7x = 540
Combining like terms, we get:
10x = 540
To solve for x, we divide both sides by 10:
x = 540/10
Simplifying, we find that:
x = 54
Therefore, S solved 54 problems that week.
To solve this problem, we need to set up a system of equations. Let's represent the number of problems S solved in a week as x and the number of problems O solved in the same week as y.
We are given that for every three problems S solves, O solves seven. This can be expressed as:
y = (7/3)x
We are also given that together, they solved 180 problems in seven days. This can be expressed as:
x + y = 180
Now we can solve this system of equations to find the value of x, which represents the number of problems S solved in a week.
Substituting the value of y from the first equation into the second equation, we have:
x + (7/3)x = 180
(10/3)x = 180
x = (3/10) * 180
x = 54
Therefore, S solved 54 problems that week.