Question

Todd has at most 14 dimes and nickels in his pocket, and the total value of the coins is more than $1. If x represents the number of dimes and y represents the number of nickels, which system of inequalities can be used to determine how many of each coin Todd has in his pocket?

a) x + y < 14; 10x + 5y > 100
b) x + y < 14; 101 + 5y > 100
c) 10x + 5y > 100; x + y < 14
d) 101 + 5y > 100; x + y < 14

Answer 1

The correct system of inequalities to represent the number of dimes (x) and nickels (y) in Todd's pocket is a) x + y < 14; 10x + 5y > 100. This accounts for having at most 14 coins with a total value over $1.

Step-by-step explanation:

The question provided by the student involves finding a system of inequalities to determine how many dimes and nickels Todd has in his pocket, given the conditions that he has at most 14 coins and the total value is more than $1. The correct system of inequalities that represents this situation is:

a) x + y < 14; 10x + 5y > 100

To solve this problem, we consider that each dime is worth 10 cents and each nickel is worth 5 cents. Thus, if x represents the number of dimes and y represents the number of nickels, the value of the dimes in cents is 10x and the value of the nickels is 5y. Combining these values together must give us more than 100 cents (or $1). Additionally, the total number of dimes and nickels, x + y, must be less than or equal to 14.