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.  

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b. an equilateral triangle inscribed in a circle

step-by-step explanation:

we are given the figure of two circles having a triangle inside.

now, we know that,

"when a figure is lying inside an another figure, then the outside figure is known as circumscribed figure and the figure lying inside is referred to as the inscribed figure".

as we see that, the circles are containing the triangle completely.

thus, the circles are the circumscribed figures and the triangle is the inscribed figure.

hence, we get, 'an equilateral triangle is inscribed in a circle'.