smc

If Jane bought one more bagel but one fewer muffin, then her total cost for the week would increase by $25$ cents. If Jane bought $1$ bagel, then she bought $4$ muffins. Her total cost for the week would be $75\cdot 1+50\cdot 4=275$ cents, or $2.75$ dollars. Clearly, she bought one more bagel but one fewer muffin at a total cost of $3.00$ dollars. Therefore, she bought $\boxed{2}$ bagels.