Kevin is 3 years older than Daniel. Two years ago, Kevin was 4 times as old as Daniel. Let k be Kevin's age and let d be Daniel's age. Which system of equations represents this situation? Choose 1 answer: (A) {[k=d+3],[k-2=4(d-2)]:} (B) {[k-2=(d-2)+3],[k=4d]:} (c) {[d-2=(k-2)+3],[d=4k]:} (D) {[d=k+3],[d-2=4(k-2)]:}

Translate first sentence: Let's translate the first sentence ＂Kevin is 3 years older than Daniel＂ into an equation. If k represents Kevin's age and d represents Daniel's age, then the equation is: k = d + 3 This equation states that Kevin's age is Daniel's age plus 3 years.Translate second sentence: Now let's translate the second sentence ＂Two years ago, Kevin was 4 times as old as Daniel＂ into an equation. Two years ago, Kevin's age would be k - 2 and Daniel's age would be d - 2. According to the sentence, Kevin's age at that time was 4 times Daniel's age at that time. So the equation is: k - 2 = 4(d - 2) This equation states that two years ago, Kevin's age was 4 times what Daniel's age was at that time.Combine equations into a system: Now we need to combine the two equations we have derived into a system of equations. The correct system of equations that represents the situation is: (A) { [k = d + 3], [k - 2 = 4(d - 2)] } This system correctly translates the given information into mathematical equations.

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Kevin is 3 years older than Daniel. Two years ago, Kevin was 4 times as old as Daniel.
Let
k be Kevin's age and let
d be Daniel's age.
Which system of equations represents this situation?
Choose 1 answer:
(A)
{[k=d+3],[k-2=4(d-2)]:}
(B)
{[k-2=(d-2)+3],[k=4d]:}
(c)
{[d-2=(k-2)+3],[d=4k]:}
(D)
{[d=k+3],[d-2=4(k-2)]:}

Kevin is $3$ years older than Daniel. Two years ago, Kevin was $4$ times as old as Daniel. $\newline$ Let $k$ be Kevin's age and let $d$ be Daniel's age. $\newline$ Which system of equations represents this situation? $\newline$ Choose $1$ answer: $\newline$ (A) $\left\{\begin{array}{l}k=d+3 \\ k-2=4(d-2)\end{array}\right.$ $\newline$ (B) $\left\{\begin{array}{l}k-2=(d-2)+3 \\ k=4 d\end{array}\right.$ $\newline$ (C) $\left\{\begin{array}{l}d-2=(k-2)+3 \\ d=4 k\end{array}\right.$ $\newline$ (D) $\left\{\begin{array}{l}d=k+3 \\ d-2=4(k-2)\end{array}\right.$

View step-by-step help

Home

Math Problems

Algebra 1

Solve a system of equations using substitution: word problems

Full solution

Q. Kevin is

3

years older than Daniel. Two years ago, Kevin was

4

times as old as Daniel.

\newline

Let

k

be Kevin's age and let

d

be Daniel's age.

\newline

Which system of equations represents this situation?

\newline

Choose

1

answer:

\newline

(A)

\left\{\begin{array}{l}k=d+3 \\ k-2=4(d-2)\end{array}\right.

\newline

(B)

\left\{\begin{array}{l}k-2=(d-2)+3 \\ k=4 d\end{array}\right.

\newline

(C)

\left\{\begin{array}{l}d-2=(k-2)+3 \\ d=4 k\end{array}\right.

\newline

(D)

\left\{\begin{array}{l}d=k+3 \\ d-2=4(k-2)\end{array}\right.

Translate first sentence: Let's translate the first sentence ＂Kevin is $3$ years older than Daniel＂ into an equation. $\newline$ If $k$ represents Kevin's age and $d$ represents Daniel's age, then the equation is: $\newline$ $k = d + 3$ $\newline$ This equation states that Kevin's age is Daniel's age plus $3$ years.
Translate second sentence: Now let's translate the second sentence ＂Two years ago, Kevin was $4$ times as old as Daniel＂ into an equation. $\newline$ Two years ago, Kevin's age would be $k - 2$ and Daniel's age would be $d - 2$ . According to the sentence, Kevin's age at that time was $4$ times Daniel's age at that time. So the equation is: $\newline$ $k - 2 = 4(d - 2)$ $\newline$ This equation states that two years ago, Kevin's age was $4$ times what Daniel's age was at that time.
Combine equations into a system: Now we need to combine the two equations we have derived into a system of equations. The correct system of equations that represents the situation is: $\newline$ (A) $\newline$ \begin{cases} k = d + 3, \ k - 2 = 4(d - 2) \end{cases} $\newline$ This system correctly translates the given information into mathematical equations.