Question

Explain why a marginal rate of substitution between two goods must equal the ratio of prices of the goods for the consumer to achieve maximum satisfaction. A consumer achieves maximum satisfaction when the marginal rate of substitution is equal to the ratio of prices because

Answer 1

use the indifference curve and budget constrain line to see that.
if the slope of indifference curve i.e. -MRS_x/MRS_y does not equal to
slope of budget constrain line i.e. -price_x/price_y. you could move along the budget constrain to reach a higher indifference curve.
that simply means you does not maximize your utility given the budget constrain.