Answered

Westonci.ca is the Q&A platform that connects you with experts who provide accurate and detailed answers. Discover in-depth answers to your questions from a wide network of experts on our user-friendly Q&A platform. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently.

Type the correct answer in each box.

For three consecutive years, Sam and Sally invested money at the start of each year.

- The first year, Sam invested [tex]$x$[/tex].
- The second year, he invested half the amount he invested the first year.
- The third year, he invested [tex]$1,000 more than \(\frac{1}{5}\) of the amount he invested the first year.

- The first year, Sally invested $[/tex]y[tex]$.
- The second year, she invested $[/tex]1,500 less than 2 times the amount Sam invested the first year.
- The third year, she invested the same amount as Sam invested the first year.

If Sam and Sally invested the same total amount at the end of three years, the amount Sam invested the first year is [tex]$\boxed{\text{ }}$[/tex].

Sagot :

GinnyAnswer
Let's solve this step by step.

1. Let [tex]\( x \)[/tex] be the amount Sam invested the first year.

2. Investments made by Sam over the three years:
- First year: [tex]\( x \)[/tex]
- Second year: [tex]\( 2x \)[/tex]
- Third year: [tex]\( \frac{x}{5} + 1000 \)[/tex]

3. Investments made by Sally over the three years:
- First year: [tex]\( 2x \)[/tex]
- Second year: [tex]\( 2x - 1500 \)[/tex]
- Third year: [tex]\( x \)[/tex]

4. Calculate the total investment by Sam over the three years:
- Total investment by Sam [tex]\( = x + 2x + \left(\frac{x}{5} + 1000\right) \)[/tex]

5. Calculate the total investment by Sally over the three years:
- Total investment by Sally [tex]\( = 2x + (2x - 1500) + x \)[/tex]

6. Equate the total investments since Sam and Sally invested the same total amount:
[tex]\[ x + 2x + \left(\frac{x}{5} + 1000\right) = 2x + (2x - 1500) + x \][/tex]

7. Simplify the equation to find [tex]\( x \)[/tex]:
- Left side: [tex]\( x + 2x + \frac{x}{5} + 1000 = \left(\frac{5x}{5} + \frac{10x}{5} + \frac{x}{5}\right) + 1000 = \frac{16x}{5} + 1000 \)[/tex]
- Right side: [tex]\( 2x + 2x - 1500 + x = 5x - 1500 \)[/tex]

- Equate the two sides:
[tex]\[ \frac{16x}{5} + 1000 = 5x - 1500 \][/tex]

- Multiply everything by 5 to clear the fraction:
[tex]\[ 16x + 5000 = 25x - 7500 \][/tex]

- Rearrange the terms to solve for [tex]\( x \)[/tex]:
[tex]\[ 5000 + 7500 = 25x - 16x \][/tex]
[tex]\[ 12500 = 9x \][/tex]
[tex]\[ x = \frac{12500}{9} \][/tex]

Hence, the amount Sam invested the first year is [tex]\( \boxed{\frac{12500}{9}} \)[/tex] dollars.
Visit us again for up-to-date and reliable answers. We're always ready to assist you with your informational needs. We appreciate your time. Please come back anytime for the latest information and answers to your questions. Westonci.ca is your go-to source for reliable answers. Return soon for more expert insights.