1. Let \( m \) be the number of miles Ian can ride.
The total cost is \( 3.50 + 0.85m \).
He has only $10, so:
\[
3.50 + 0.85m \leq 10
\]
Subtract 3.50 from both sides:
\[
0.85m \leq 6.50
\]
Divide by 0.85:
\[
m \leq \frac{6.50}{0.85} \approx 7.647
\]
Since he can’t ride a fraction of a mile in this context, he can ride at most 7 miles.
Answer: 7
2. Let \( c \) be the number of candies Hannah can buy.
She spends $5 on a bracelet and $0.75 per candy, with a total of $10.
So:
\[
5 + 0.75c \leq 10
\]
Subtract 5:
\[
0.75c \leq 5
\]
Divide by 0.75:
\[
c \leq \frac{5}{0.75} = \frac{20}{3} \approx 6.666...
\]
She can buy at most 6 candies (since she can’t buy a fraction).
Answer: 6
3. Let \( t \) be the number of tickets they need to sell.
Each ticket is $5, and they must spend $25 on decorations.
They want to make at least $350, so:
\[
5t - 25 \geq 350
\]
Add 25 to both sides:
\[
5t \geq 375
\]
Divide by 5:
\[
t \geq 75
\]
They must sell at least 75 tickets.
Answer: 75
4. Let \( w \) be the number of weeks Trisha should save.
She saves $25 per week and already has $100.
She needs at least $350 for vacation and wants to have over $100 left after the trip.
So total money after saving: \( 100 + 25w \)
After spending $350, she must have more than $100 left:
\[
100 + 25w - 350 > 100
\]
Simplify:
\[
25w - 250 > 100
\]
Add 250:
\[
25w > 350
\]
Divide by 25:
\[
w > 14
\]
Since she must save for more than 14 weeks, and weeks are whole numbers, she needs at least 15 weeks.
Answer: 15
Parent Tip: Review the logic above to help your child master the concept of inequality problems worksheet.
