Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Kevin is 4 times as old as Daniel and is also 6 years older than Daniel.
How old is Daniel?

Kevin is \(4\) times as old as Daniel and is also \(6\) years older than Daniel. $\newline$ How old is Daniel?

View step-by-step help

View step-by-step help

Solve a system of equations using any method: word problems

Full solution

Q. Kevin is \(4\) times as old as Daniel and is also \(6\) years older than Daniel.

\newline

How old is Daniel?

Equation $1$ : Kevin's age in terms of Daniel's age: Let's denote Daniel's age as $D$ and Kevin's age as $K$ . According to the problem, Kevin is $4$ times as old as Daniel, which gives us the first equation: $\newline$ $K = 4D$
Equation $2$ : Kevin's age in terms of Daniel's age: The problem also states that Kevin is $6$ years older than Daniel, which gives us the second equation: $\newline$ $K = D + 6$
Setting the equations equal to each other: Now we have a system of two equations: $\newline$ $1$ ) $K = 4D$ $\newline$ $2$ ) $K = D + 6$ $\newline$ We can set these two equations equal to each other since they both equal $K$ . $\newline$ $4D = D + 6$
Solving for Daniel's age: Next, we solve for $D$ by subtracting $D$ from both sides of the equation: $\newline$ $4D - D = D + 6 - D$ $\newline$ $3D = 6$
Finding the value of D: Now, we divide both sides by $3$ to find the value of D: $\newline$ $\frac{3D}{3} = \frac{6}{3}$ $\newline$ $D = 2$

More problems from Solve a system of equations using any method: word problems

Question

Solve using substitution.

5x - 2y = -7

x = -5

Posted 5 months ago

Question

(1,1)

a solution to this system of equations?

\newline

4x + 10y = 14

\newline

x + 6y = 7

\newline

\newline

\newline

Posted 5 months ago

Question

Which describes the system of equations below?

\newline

y = –3x + 9

\newline

y = –3x + 9

\newline

\newline

\text{(A) consistent and independent}

\newline

\text{(B) consistent and dependent}

\newline

\text{(C) inconsistent}

Posted 5 months ago

Question

Solve using elimination.

\newline

7x - 8y = -17

\newline

-7x + 3y = 2

\newline

(\_\_\_\_, \_\_\_\_)

Posted 5 months ago

Question

\newline

x = -2

\newline

-2x + 2y = -8

\newline

(\_\_\_\_, \_\_\_\_)

Posted 9 months ago

Question

Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.

\newline

At a community barbecue, Mrs. Wilkerson and Mr. Hogan are buying dinner for their families. Mrs. Wilkerson purchases

3

hot dog meals and

3

hamburger meals, paying a total of

\$36

. Mr. Hogan buys

1

hot dog meal and

3

hamburger meals, spending

\$26

in all. How much do the meals cost?

\newline

Hot dog meals cost

\$

_______ each, and hamburger meals cost

\$

Posted 9 months ago

Question

Solve the system of equations by substitution.

\newline

-3x - y - 3z = -11

\newline

z = 5

\newline

x - y + 3z = 19

\newline

(____.____,____)

Posted 5 months ago

Question

Solve the system of equations by elimination.

\newline

x - 3y - 2z = 10

\newline

3x + 2y + 2z = 14

\newline

2x - 3y - 2z = 16

\newline

(\_,\_,\_)

Posted 5 months ago

Question

Solve the system of equations.

\newline

y = x^2 + 36x + 3

\newline

y = 22x - 37

\newline

Write the coordinates in exact form. Simplify all fractions and radicals.

\newline

(\_,\_)

\newline

(\_,\_)

Posted 5 months ago

Question

Solve the system of equations.

\newline

y = -x - 24

\newline

x^2 + y^2 = 488

\newline

Write the coordinates in exact form. Simplify all fractions and radicals.

\newline

(\_,\_)

\newline

(\_,\_)

Posted 5 months ago

Related topics

Algebra - Order of Operations Algebra - Distributive Property `X` and `Y` Axes Geometry - Scalene Triangle Common Multiple Geometry - Quadrant