🎵 Did You Know? — Len Kagamine + Baking!
In the Vocaloid fandom, Len Kagamine is famous for loving bananas 🍌. If Len bakes banana bread and each loaf needs 3 bananas, and he already has 4 bananas at home, then after buying b bunches (6 bananas each), he has: y = 6b + 4 bananas. The y-intercept (4) = bananas he started with. The slope (6) = bananas per bunch. That's a real-world linear equation! 🍞
✏️ Worked Example — Read This First!
A plumber charges a $65 call-out fee plus $45 per hour. Write an equation for the total cost C after h hours. Then find the cost for a 3-hour job.
1
Identify the slope (rate).
$45 per hour → m = 45
$45 per hour → m = 45
2
Identify the y-intercept (starting value).
$65 flat fee → b = 65 (cost when h = 0)
$65 flat fee → b = 65 (cost when h = 0)
3
Write the equation.
C = 45h + 65
C = 45h + 65
4
Substitute h = 3 to find the cost.
C = 45(3) + 65 = 135 + 65 = $200
C = 45(3) + 65 = 135 + 65 = $200
C = 45h + 65 | 3-hour job = $200
💡 Strategy for word problems:
1. What is changing? → that's your variable (x)
2. What is the rate of change? → that's your slope (m)
3. What is the starting value? → that's your y-intercept (b)
4. Write y = mx + b using the context's variable names
1. What is changing? → that's your variable (x)
2. What is the rate of change? → that's your slope (m)
3. What is the starting value? → that's your y-intercept (b)
4. Write y = mx + b using the context's variable names
EasyQuestions 1–3 — Write the equation
Question 1 EasySee Answer →
Alishba's cat water fountain holds 200 mL. It drains at a rate of 25 mL per hour.
a) Write an equation for the amount of water W (in mL) remaining after h hours.
b) How much water is left after 3 hours?
a) Write an equation for the amount of water W (in mL) remaining after h hours.
b) How much water is left after 3 hours?
Working space
Question 2 EasySee Answer →
Alishba is saving money to buy a Len Kagamine figure. She already has $60 saved and puts away $15 every week.
a) Write an equation for her total savings S after w weeks.
b) How much will she have after 8 weeks?
a) Write an equation for her total savings S after w weeks.
b) How much will she have after 8 weeks?
Working space
Question 3 EasySee Answer →
A baking supply website charges a $35 membership fee plus $0.05 per gram of sprinkles ordered.
a) Write an equation for cost C when ordering g grams of sprinkles.
b) What is the cost of ordering 400 grams?
a) Write an equation for cost C when ordering g grams of sprinkles.
b) What is the cost of ordering 400 grams?
Working space
MediumQuestions 4–7
Question 4 MediumSee Answer →
Miku fills a balloon with helium. The balloon rises at 2.5 feet per second starting from ground level (0 feet).
a) Write an equation for the height H after s seconds.
b) What is the height after 12 seconds?
c) How many seconds to reach 50 feet? (Solve the equation.)
a) Write an equation for the height H after s seconds.
b) What is the height after 12 seconds?
c) How many seconds to reach 50 feet? (Solve the equation.)
Working space
Question 5 MediumSee Answer →
A cat shelter charges a $40 adoption fee plus $2 per day for boarding.
a) Write an equation for total cost C after d days of boarding.
b) Find the total cost for 7 days.
c) If someone paid $64, how many days was the cat boarded? (Solve for d.)
a) Write an equation for total cost C after d days of boarding.
b) Find the total cost for 7 days.
c) If someone paid $64, how many days was the cat boarded? (Solve for d.)
Working space
Question 6 MediumSee Answer →
Rin starts with $450 in her baking supply fund and spends $30 per week.
a) Write an equation for the amount A remaining after w weeks.
b) Find the x-intercept and explain what it means in context.
c) Find the y-intercept and explain what it means in context.
a) Write an equation for the amount A remaining after w weeks.
b) Find the x-intercept and explain what it means in context.
c) Find the y-intercept and explain what it means in context.
Working space
Question 7 MediumSee Answer →
A Vocaloid concert sells student tickets for $6 and adult tickets for $9. Total ticket revenue was $540.
a) Write an equation in Standard Form where s = student tickets and a = adult tickets.
b) Find the x-intercept (s-axis) and interpret what it means.
c) Find the y-intercept (a-axis) and interpret what it means.
a) Write an equation in Standard Form where s = student tickets and a = adult tickets.
b) Find the x-intercept (s-axis) and interpret what it means.
c) Find the y-intercept (a-axis) and interpret what it means.
Working space
HardQuestions 8–10 — Multi-part challenges
Question 8 HardSee Answer →
At 7 AM, the temperature outside is 48°F. It increases at a constant rate of 4°F per hour.
a) Write an equation for temperature T where h = hours after 7 AM.
b) What is the temperature at noon?
c) At what time does the temperature reach 72°F?
d) What was the temperature at 5 AM (before 7 AM)?
a) Write an equation for temperature T where h = hours after 7 AM.
b) What is the temperature at noon?
c) At what time does the temperature reach 72°F?
d) What was the temperature at 5 AM (before 7 AM)?
Working space — careful with negative h values for "before" times
Question 9 HardSee Answer →
Alishba's cat fountain holds 25,000 mL. It drains at 500 mL per hour.
a) Write an equation for water remaining W after h hours.
b) When is the fountain exactly half empty?
c) Find the x-intercept. What does it mean?
d) Find the y-intercept. What does it mean?
a) Write an equation for water remaining W after h hours.
b) When is the fountain exactly half empty?
c) Find the x-intercept. What does it mean?
d) Find the y-intercept. What does it mean?
Working space
Question 10 HardSee Answer →
Two balloon-making kits are on sale:
Kit A: $25 to buy + $0.30 per balloon made.
Kit B: $40 to buy + $0.15 per balloon made.
a) Write equations for the total cost of each kit after making n balloons.
b) Find the number of balloons at which both kits cost the same. Show your algebra.
c) Which kit is cheaper if you plan to make 150 balloons?
Kit A: $25 to buy + $0.30 per balloon made.
Kit B: $40 to buy + $0.15 per balloon made.
a) Write equations for the total cost of each kit after making n balloons.
b) Find the number of balloons at which both kits cost the same. Show your algebra.
c) Which kit is cheaper if you plan to make 150 balloons?
Working space
🐱 You Made It to the End! Reward Yourself!
Completing all 6 topics means you've practised 60 questions covering every linear equation skill tested in Frisco ISD Algebra 1! That's a serious achievement. 🎉 Fun cat fact to celebrate: cats have 230 bones (humans have 206). If a skeleton museum charges $3 per bone displayed, Algebra helps you figure out that displaying a full cat skeleton costs 3 × 230 = $690. That's just substitution — you've got this! 😸