Question

Can someone help me with this problem please

Applying the Solution to a 3X3 System


At a family reunion, there only blood relatives, consisting of children, parents, and grandparents, in attendance. There were 400 people total. There were twice as many parents as grandparents, and 50 more children than parents. How many children, parents, and Grandparents were in attendance?

Show up all steps please

Answer 1

• 190 children
• 140 parents
• 70 grandparents

Explanation:

You want the numbers of children, parents, and grandparents, given these relations:

• the total number is 400
• twice as many parents as grandparents
• 50 more children than parents.

Setup

Using c, p, g to represent the numbers of children, parents, and grandparents, we can write these equations to describe the relations:

c +p +g = 400

p = 2g

c = p +50

Solution

Using the last equation to substitute for c in the first, we have ...

(p+50) +p +g = 400

2p +g = 350 . . . . . . . . . subtract 50, collect terms

Using the second equation to substitute for p in this equation gives ...

2(2g) +g = 350

5g = 350 . . . . . . . . . . collect terms

g = 350/5 = 70 . . . . . divide by the coefficient of g

Now, we can find the values of the other variables.

p = 2g = 2(70) = 140

c = p +50 = 140 +50 = 190

There were 190 children, 140 parents, and 70 grandparents in attendance.

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Additional comment

We find it convenient to use the matrix function of a calculator to reduce the augmented matrix of the equation coefficients. The attachment shows a solution that agrees with our work above.

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