Jachin is saving to buy a new tablet that costs more than $400. He already has $85 in his piggy bank, and he is able to put $25 in his bank once a week when he gets paid for mowing lawns.
The inequality that represents this situation is 25w+85>400,
where w represents the number of weeks Jachin makes a deposit into his piggy bank.
What does the solution for the inequality mean in relation to this situation?
The solution is w>19.4. It will take Jachin a minimum of 20 weeks to save enough money to buy the tablet.
The solution is w>19.4. It will take Jachin no more than 20 weeks to save enough money to buy the tablet.
The solution is w>12.6. It will take Jachin a minimum of 12.6 weeks to save enough money to buy the tablet.**
The solution is w>12.6. It will take Jachin a minimum of 13 weeks to save enough money to buy the tablet.
The solution is w>19.4. It will take Jachin a minimum of 19.4. weeks to save enough money to buy the tablet.
The solution is w>12.6. It will take Jachin no more than 13 weeks to save enough money to buy the tablet.
The solution is w>12.6. It will take Jachin a minimum of 13 weeks to save enough money to buy the tablet.
The correct answer is:
The solution is w>12.6. It will take Jachin a minimum of 13 weeks to save enough money to buy the tablet.
The correct answer is: The solution is w>12.6. It will take Jachin a minimum of 12.6 weeks to save enough money to buy the tablet.
To understand why this is the correct answer, let's break down the inequality: 25w + 85 > 400.
- The left side of the inequality, 25w, represents the total amount of money Jachin can save in w weeks. Since he can save $25 each week, the total amount saved after w weeks is 25w.
- The right side of the inequality, 400, represents the cost of the tablet.
- The inequality symbol > represents "greater than", indicating that the total amount saved must be greater than the cost of the tablet.
To find the solution for w, we can subtract 85 from both sides of the inequality to isolate 25w:
25w > 400 - 85
25w > 315
Then, we can divide both sides of the inequality by 25:
w > 315/25
Simplifying the right side gives:
w > 12.6
This means that Jachin needs to save for at least 12.6 weeks to have enough money to buy the tablet. Since time must be a whole number, he would need to save for a minimum of 13 weeks.