Kate already has $55 dollars in her savings account. If
she puts $5 per week in her account, write and solve an
inequality to determine how many weeks she must save to
have at least $100 in her account. Interpret the solution.
let x be number of weeks
total = 55 + 5x
if you want to find the total for $100, isolate for the variable x
100 = 55 + 5x
(subtract 55 from both sides)
45 = 5x
(divide both sides by 5 to isolate x)
9 = x
therefore it will take 9 weeks to get $100
and you can check this by putting 9 back into the equation
total = 55 + 5(9)
total = 100
Wow! We are definitely thorough as tutors : ) From the gentle nudge, to the exceptionally helpful : )
Hats off Ms Sue and Mat : )
55 + 5w > 100
5w = 45
w = ?
To determine how many weeks Kate must save to have at least $100 in her account, we can write an inequality.
Let's define "x" as the number of weeks Kate saves. Each week, she adds $5 to her account. We can represent this as 5x.
We also know that Kate already has $55 in her account, so we can add that to our equation.
Thus, we have the inequality:
55 + 5x ≥ 100
To solve this inequality, we need to isolate x on one side. We'll start by subtracting 55 from both sides:
5x ≥ 100 - 55
5x ≥ 45
Next, we can divide both sides by 5 to find the value of x:
x ≥ 45/5
x ≥ 9
Therefore, Kate must save for at least 9 weeks to have at least $100 in her account.
Interpretation: The solution tells us that if Kate saves for at least 9 weeks, contributing $5 per week on top of her existing $55, she will have at least $100 in her account.
What is your first attempt?
Even if you just add the number 5 to 55 until you get up to 100, you will have a starting idea.
What do you think?