Please solve the following two word problems

Question

#1  Find three consecutive even integers such that five times the samllest is four times the largest.

 

#2  A cashier always starts the day with $60 in pennies, nickels, dimes, and quarters.  she begins with five times as many pennies as quarters, and the number of nickels and dimes are both twice the number of quarters.  How many pennies does she start with?

Answer 1

#1

Consecutive even numbers are two apart, so if the first is x, then the second is x+2, and the third is x+4.

For example, 4, 4+2=6, 4+4=8 are three consecutive even numbers.

 

The second part of the sentence gives a relationship between the first and third:

 

five times the smallest is four times the largest.

  5      *           x         =   4      *         (x+4)

 

5x = 4(x+4)

 

Distribute and solve for x, then add two and four to find the next two even numbers.

 

#2

 

We have four types of coins, and we can relate them all to the number of quarters.

 

The number of quarters:

q

 

There are five times as many pennies as quarters:

p = 5 * q = 5q

 

The number of nickels and dimes are both twice the number of quarters:

n = 2 * q = 2q

d = 2 * q = 2q

 

Each penny is worth 1 cent, nickels are 5, dimes are 10, and quarters are 25 cents. 60 dollars is 6000 cents.

 

1p + 5n + 10d + 25q = 6000

1(5q) + 5(2q) + 10(2q) + 25q = 6000

 

Multiply and add like terms, then solve for q. Check what the problem is asking for: the number of pennies. Plug q into the equation for pennies to find your answer.