Linear Equations and Inequalities on One Variable

Main topic: Linear Equations and Inequalities in One Variable

Subtopic: Solve applied problems involving linear equations   

John has $9.60 in pennies and nickels. If there are thrice as many nickels as pennies, how many pennies does John have? How many nickels does he have?

A. 360 Pennies and 120 nickels

B. 120 Pennies and 360 nickels

C. 60 Pennies and 180 nickels

D. 180 Pennies and 60 nickels

Answer: C

Rationale

Let p be the number of pennies. There are thrice as many nickels as pennies. So, there are 3p nickels.

First step is converting all the currencies in the same unit – ‘cent’.

As $1 = 100 cents, $ 9.60 = 960 cents

As 1 penny = 1 cent, p pennies = p cents

As 1 nickel = 5 cents, 3p nickels = 15p cents

Second step is constructing an equation using given information.

Number of cents for pennies + number of cents for nickels = Total number of cents.

So equation is,

 p + 15p = 960

After simplifying left side,

16p = 960

Or p = 60

Therefore, number of pennies = p = 60 and number of nickels = 3p = 3*60 = 180.

Answer option A is incorrect. Check the given relation between pennies and nickel. The number of nickels is three times the number of pennies.

Answer option B is incorrect. Check the given relation between pennies and nickel. The number of nickels is three times the number of pennies.

Answer option D is incorrect. Check the given relation between pennies and nickel in the final step.