Answer:
P(picking a quarter) = x / 32
Step by step explanation:
To find the probability of Suruchi picking a quarter, we need to know how many quarters she has in her purse and the total number of coins in her purse. Let's assume that Suruchi has only quarters, dimes, and nickels in her purse.
We know that the total value of change in Suruchi's purse is $1.64. Let's express the value of each coin in cents:
A quarter is worth 25 cents
A dime is worth 10 cents
A nickel is worth 5 cents
Let's represent the number of quarters, dimes, and nickels in Suruchi's purse by the variables q, d, and n, respectively. We can set up an equation based on the value of the coins:
25q + 10d + 5n = 164
Simplifying the equation by dividing both sides by 5, we get:
5q + 2d + n = 32
Since we don't know the specific values of q, d, and n, we can't determine the exact probability of Suruchi picking a quarter. However, we can use the fact that the total number of coins in Suruchi's purse is 32 (since the equation above tells us that the sum of the number of each type of coin must add up to 32).
Let's assume that Suruchi has x quarters in her purse. Then the total number of coins in her purse is:
x + (32 - x) = 32
Simplifying, we get:
x = 32 - (32 - x)
x = x
This tells us that the number of quarters in Suruchi's purse doesn't affect the total number of coins in her purse. Therefore, the probability of Suruchi picking a quarter is simply the ratio of the number of quarters to the total number of coins:
P(picking a quarter) = number of quarters / total number of coins
P(picking a quarter) = x / 32
Since we don't know the specific value of x, we can't calculate the probability. However, we do know that the probability will be between 0 and 1, since it represents a fraction of the total number of coins in Suruchi's purse.