Q24. The sum of 3 numbers is 20. The ... [FREE SOLUTION]

91影视

Chapter 3: Q24. (page 143)

The sum of 3 numbers is 20. The second number is 4 times the first and the sum of the first and third is 8. Find the numbers.

Short Answer

Expert verified

The three numbers are $3, 12,$ and .5

Step by step solution

– First construct a system of equations corresponding to the given situation.

Let the three numbers be $x, y,$ and $z$ .

The sum of three numbers is 20, so, mathematically it can be written as $x + y + z = 20$

The second number is 4 times the first number.

This can be mathematically written as $y = 4 x 鈬� 4 x - y = 0$ .

The sum of first and third number is 8.

This can be mathematically written as $x + z = 8$ .

So, the system of equations will be:

\begin{matrix} x + y + z = 20 \\ 4 x 鈭� y = 0 \\ x + z = 8 \end{matrix}

– Use the elimination method to get the system of equations in two variables.

Add the $e q u a t i o n x + y + z = 20$ to the equation $4 x - y = 0$ .

localid="1647998459082" $\begin{array}{l} \underset{}{\begin{array}{l} 鈥夆赌� x + y + z = 20 \\ 4 x 鈭� y + 鈥夆赌夆€夆赌� = 鈥夆赌� 0 \end{array}} \\ 5 x + 0 鈥夆赌� + z = 20 \end{array}$

So, the resultant equation is $5 x + z = 20$

Subtract the equation $5 x + z = 20$ from the equation $x + z = 8$

$\begin{array}{l} \underline{\begin{array}{l} 鈥夆赌夆€夆赌� 5 x + z = 20 \\ (鈭�) 鈥夆赌� x + z = 鈥夆赌夆€� 8 \end{array}} \\ 鈥夆赌夆€夆赌� 4 x + 0 = 12 \end{array}$

– Find the values of x,y and z.

Solve $4 x = 12$ for $x$ :

$\begin{matrix} 4 x = 12 \\ \frac{4 x}{4} = \frac{12}{4} 鈥夆赌夆€夆赌夆€塂ividebothsidesby 4 \\ x = 3 \end{matrix}$

Substitute $x = 3 i n 4 x - y = 0$ and find the value of $y$

$\begin{matrix} 4 x 鈭� y = 0 \\ 4 (3) 鈭� y = 0 鈥夆赌夆€夆赌夆€夆赌夆€夆赌夆€夆赌夆€夆赌夆€夆赌夆€夆赌夆€夆赌塖ubstitute 3 for x \\ 12 鈭� y = 0 鈥夆赌夆€夆赌夆€夆赌夆€夆赌夆€夆赌夆€夆赌夆€夆赌夆€夆赌夆€塖implify \\ 鈭� y = 鈭� 12 鈥夆赌夆€夆赌夆€夆赌夆€夆赌夆€夆赌夆€夆赌夆€夆赌塖ubtract 12 frombothsides \\ y = 12 鈥夆赌夆€夆赌夆€夆赌夆€夆赌夆€夆赌夆€夆赌夆€夆赌夆€夆赌塂ividebothsidesby 鈭� 1 \end{matrix}$

Substitutelocalid="1647998527720" $x = 3 i n x + z = 8$ and find the value of $z$

$\begin{matrix} x + z = 8 \\ 3 + z = 8 鈥夆赌夆€夆赌夆€夆赌夆€夆赌夆€夆赌夆€塻ubstitute 3 for x \\ z = 5 鈥夆赌夆€夆赌夆€夆赌夆€夆赌夆€塖ubtract 3 鈥塮谤辞尘产辞迟丑蝉颈诲别蝉 \end{matrix}$

Hence, the solution of the given system of equations is $(x, y, z) = (3, 12, 5)$ .

So, the three numbers are $3, 12, a n d 5$ .

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

91影视

The sum of 3 numbers is 20. The second number is 4 times the first and the sum of the first and third is 8. Find the numbers.

Short Answer

Step by step solution

– First construct a system of equations corresponding to the given situation.

– Use the elimination method to get the system of equations in two variables.

– Find the values of x,y and z.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Pure Maths

Calculus

Decision Maths

Mechanics Maths

Geometry

Study anywhere. Anytime. Across all devices.