Trip has 15 coins worth 95 cents. Four of the coins are each worth twice as much as the rest. Construct a math argument to justify the conjecture that trip has 11 nickels and 4 dimes

We can formulate a simple algebraic expression to solve for the values. Let the value of the smaller coin be denoted x, and the larger coin thus 2x. Therefore, we can say that 95 = 11x + 4*2x (since the prompt states that there are 4 of the larger coins, there are thus 11 of the smaller ones, since the prompt says 15 in total). Thus, 95 = 19x, and x = 5 cents, thus 2x = 10 cents. As such, the small coin (x) is a nickel (5 cents) and the large coin (2x) is a dime (10 cents)