Linda has some nickels and dimes amounting $2.90. The number of dimes is 1 less than twice the number of nickels. How many coins of each kind does she have?

Question

let me know how you did it ! thanks

Answer 1

First, set this up as an algebra problem, with the number of nickels as the variable x. The coefficients could be in dollars (i.e. 0.10 & 0.05) or pennies (10 & 5) - it would work just fine either way. For visual clarity & ease of computing, let's not use the decimal points:

 

5x + 10(2x-1) = 290

 

Let's briefly analyze this equation. It means "5 times the number of nickels plus 10 times one less than twice the number of nickels equals 290." Make sense?

 

Now manipulate it using the algebra you already know.

 

Distribute: 5x + 20x - 10 = 290

Combine like terms: 25x - 10 = 290

Add 10 to both sides: 25x = 300

Divide both sides by 25: x = 12

 

There are 12 nickels, so we use the equation to determine how many dimes:

 

5x + 10(2(12)-1) = 290

5(12) + 10(24-1) = 290

 

60 + 10(23) = 290

10(23) = 290 - 60

10(23) = 230

 

There are 23 dimes.