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Answer :
Let's work through the problem step-by-step:
1) How old was Kwesi 7 years ago?
- If Kwesi is currently [tex]\( x \)[/tex] years old, then 7 years ago he would have been [tex]\( x - 7 \)[/tex] years old.
2) How old will Kwesi be in 15 years from now?
- If Kwesi is currently [tex]\( x \)[/tex] years old, then in 15 years he will be [tex]\( x + 15 \)[/tex] years old.
3) If his age in 15 years will be four times his age 7 years ago, how old is he now?
Let's set up the equation based on the information given:
- In 15 years, Kwesi will be [tex]\( x + 15 \)[/tex].
- Seven years ago, he was [tex]\( x - 7 \)[/tex].
According to the problem, in 15 years his age will be four times his age 7 years ago. So we set up the equation:
[tex]\[
x + 15 = 4(x - 7)
\][/tex]
Now let's solve this equation step-by-step:
1. Start by expanding the equation:
[tex]\[
x + 15 = 4(x - 7)
\][/tex]
2. Distribute the 4 on the right side:
[tex]\[
x + 15 = 4x - 28
\][/tex]
3. Move all terms involving [tex]\( x \)[/tex] to one side by subtracting [tex]\( x \)[/tex] from both sides:
[tex]\[
15 = 3x - 28
\][/tex]
4. Add 28 to both sides to isolate the term with [tex]\( x \)[/tex]:
[tex]\[
43 = 3x
\][/tex]
5. Solve for [tex]\( x \)[/tex] by dividing both sides by 3:
[tex]\[
x = \frac{43}{3}
\][/tex]
So, Kwesi is [tex]\(\frac{43}{3}\)[/tex] years old now. This is approximately 14 years and 4 months if you want to express it in years and months.
1) How old was Kwesi 7 years ago?
- If Kwesi is currently [tex]\( x \)[/tex] years old, then 7 years ago he would have been [tex]\( x - 7 \)[/tex] years old.
2) How old will Kwesi be in 15 years from now?
- If Kwesi is currently [tex]\( x \)[/tex] years old, then in 15 years he will be [tex]\( x + 15 \)[/tex] years old.
3) If his age in 15 years will be four times his age 7 years ago, how old is he now?
Let's set up the equation based on the information given:
- In 15 years, Kwesi will be [tex]\( x + 15 \)[/tex].
- Seven years ago, he was [tex]\( x - 7 \)[/tex].
According to the problem, in 15 years his age will be four times his age 7 years ago. So we set up the equation:
[tex]\[
x + 15 = 4(x - 7)
\][/tex]
Now let's solve this equation step-by-step:
1. Start by expanding the equation:
[tex]\[
x + 15 = 4(x - 7)
\][/tex]
2. Distribute the 4 on the right side:
[tex]\[
x + 15 = 4x - 28
\][/tex]
3. Move all terms involving [tex]\( x \)[/tex] to one side by subtracting [tex]\( x \)[/tex] from both sides:
[tex]\[
15 = 3x - 28
\][/tex]
4. Add 28 to both sides to isolate the term with [tex]\( x \)[/tex]:
[tex]\[
43 = 3x
\][/tex]
5. Solve for [tex]\( x \)[/tex] by dividing both sides by 3:
[tex]\[
x = \frac{43}{3}
\][/tex]
So, Kwesi is [tex]\(\frac{43}{3}\)[/tex] years old now. This is approximately 14 years and 4 months if you want to express it in years and months.
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