A machine produces 7/10 of a part every 7/20 of a minute. What is its production rate per minute? — 2 parts/min.(7/10) ÷ (7/20) = (7/10) × (20/7) = 140/70 = 2 parts per minute.
A worker earns $5/6 for every 5/18 of an hour. What is the hourly wage? — $3 per hour.(5/6) ÷ (5/18) = (5/6) × (18/5) = 90/30 = $3 per hour.
A cyclist bikes 9/4 miles every 3/8 of an hour. What is the speed in miles per hour? — 6 mph.(9/4) ÷ (3/8) = (9/4) × (8/3) = 72/12 = 6 mph.
A leaking pipe loses 7/12 of a gallon in 7/24 of an hour. How many gallons per hour does it lose? — 2 gal/hr.(7/12) ÷ (7/24) = (7/12) × (24/7) = 168/84 = 2 gallons per hour.
A garden hose fills 3/8 of a bucket in 3/4 of a minute. How long to fill 1 full bucket? — 2 minutes.Rate = (3/8) ÷ (3/4) = (3/8) × (4/3) = 1/2 bucket/min. Time to fill 1 bucket = 1 ÷ (1/2) = 2 minutes.
A truck uses 5/6 of a gallon of fuel to travel 5/3 of a mile. What is the fuel efficiency (miles per gallon)? — 2 miles per gallon.(5/3) ÷ (5/6) = (5/3) × (6/5) = 30/15 = 2 miles per gallon.
A proportional graph has two points: (3, 12) and (n, 20). What is n? — 5.k = 12/3 = 4. So y = 4x. When y = 20, x = 20/4 = 5.
Two linear equations: Line A is y = 3x and Line B is y = 3x + 2. Which passes through the origin? — Line A only.Line A: y = 3(0) = 0, so it passes through (0,0). Line B: y = 3(0) + 2 = 2, so it passes through (0,2), not the origin.
A jacket costs $120 after a 25% discount. What was the original price? — $160.After 25% off, you pay 75% of original. 120 = 0.75 × original → original = 120/0.75 = $160.
A $200 bike is discounted 15%, then a 6% tax is applied to the sale price. What is the final price? — $180.20.Sale price: $200 × 0.85 = $170. Tax: $170 × 0.06 = $10.20. Final: $170 + $10.20 = $180.20.
A restaurant bill is $60. An 8% tax and 15% tip are each applied to the original bill. What is the total? — $73.80.Tax = $60 × 0.08 = $4.80. Tip = $60 × 0.15 = $9.00. Total = $60 + $4.80 + $9.00 = $73.80.
A phone originally costs $800, is discounted 20%, then the sale price is taxed 10%. What is the final price? — $704.After 20% off: $800 × 0.80 = $640. After 10% tax: $640 × 1.10 = $704.
You borrow $3,000 at 8% simple interest per year. How much interest do you pay after 18 months? — $360.18 months = 1.5 years. I = 3000 × 0.08 × 1.5 = $360.
A $350 TV is discounted 10%, then discounted another 10% on the new price. Is this the same as 20% off? — No, the second discount applies to a lower price, so total is less than 20% off.First discount: $350 × 0.90 = $315. Second: $315 × 0.90 = $283.50. Actual discount: $66.50/$350 = 19% off — less than 20%.
A $120 jacket is on sale with a coupon for 25% off. You also use a loyalty card for an extra 10% off the sale price. How much do you pay? — $81.After 25%: $120 × 0.75 = $90. After extra 10%: $90 × 0.90 = $81.