Write what the expressions below best represent within the context of the word problem. mark had 3 times as many quarters as nickels. he had $1.60 in all. how many nickels and how many quarters did mark have? x represents . 3x represents

x represents the amount of nickels, 3x represents the amount of quarters. Mark had 8 nickels and 24 quarters

Step-by-step explanation:

Let's understand the given information by developing a mathematical expression.

The problem can be divided into three parts, two information statements and one question.

Given information:

1. Mark had 3 times as many quarters as nickels: this means that for each nickel, Mark had 3 quarters. Because the amount of quarters depends on the amount of nickels, we can establish that if Mark had x nickels, then he had 3x quarters.

2. Mark had $ 1.60 in all: this means that by adding the quarters and the nickels, Mark had $1.60 in all. Because we defined before that x nickels implies 3x quarters, then an expresion for Mark's money is:

$1.60=3x+x; being x the amount of nickels Mark had. Because the total amount of money is in dollars, then considering that 20 nickels is a dollar, we can re-write the expression as:

32=3x+x; being x the amount of nickels.

Given question:

How many nickels and how many quarters did Mark have?

Solving the previous equation, 32=3x+x, we obtain:

32=4x which means x=32/4=8.

So x=8 means that Mark had 8 nickels, and because Mark also had 3x quarters, then Mark had 8*3=24 quarters.

In summary, x represents the amount of niquels, 3x represents the amount of quarters, and since Mark had $1.60 in all, he had 8 nickels and 24 quarters.