This algebra 1 units worksheet answer key solves all 23 problems of the units, quantities and modeling worksheet step by step.
Every solution below shows the unit chain, so check that your units cancel the same way. Compare your numbers step by step, and review the lesson if a conversion factor was flipped or a rounded value was used too early.
Algebra 1 Units Worksheet Answer Key: problems 1–5
Problem 1: Miles to feet
Multiply by the factor that cancels miles: \(5\text{ mi}\times \frac{5280\text{ ft}}{1\text{ mi}}=26{,}400\text{ ft}\).
26,400 ft
Problem 2: Hours to seconds
\(3.5\text{ h}\times \frac{60\text{ min}}{1\text{ h}}\times \frac{60\text{ s}}{1\text{ min}}=3.5\times 3600\text{ s}=12{,}600\text{ s}\).
12,600 s
Problem 3: Inches to yards
\(72\text{ in}\times \frac{1\text{ yd}}{36\text{ in}}=2\text{ yd}\).
2 yd
Problem 4: Miles per hour to feet per second
\(45\,\frac{\text{mi}}{\text{h}}\times \frac{5280\text{ ft}}{1\text{ mi}}\times \frac{1\text{ h}}{3600\text{ s}}=\frac{237{,}600}{3600}\,\frac{\text{ft}}{\text{s}}=66\,\frac{\text{ft}}{\text{s}}\).
66 ft/s
Problem 5: Gallons to cups
\(2.5\text{ gal}\times \frac{4\text{ qt}}{1\text{ gal}}\times \frac{4\text{ cups}}{1\text{ qt}}=2.5\times 16=40\text{ cups}\).
40 cups
Algebra 1 Units Worksheet Answer Key: problems 6–10
Problem 6: Units of a product
\(\frac{\$14}{1\text{ h}}\times \frac{18\text{ h}}{1\text{ week}}\times 6\text{ weeks}\): hours cancel and weeks cancel, leaving dollars.
\(14\times 18\times 6=1512\).
\(\$1{,}512\)
Problem 7: Cost per mile
\(\frac{\$3.50}{1\text{ gal}}\times \frac{1\text{ gal}}{28\text{ mi}}=\frac{\$3.50}{28\text{ mi}}=\$0.125\text{ per mi}\).
\(\$0.125\) per mile (12.5 cents)
Problem 8: Weight of water
\(62.4\,\frac{\text{lb}}{\text{ft}^{3}}\times 8\text{ ft}^{3}=499.2\text{ lb}\); cubic feet cancel.
499.2 lb
Problem 9: Acres of a field
Area: \(330\times 330=108{,}900\text{ ft}^{2}\).
\(108{,}900\text{ ft}^{2}\times \frac{1\text{ acre}}{43{,}560\text{ ft}^{2}}=2.5\text{ acres}\).
2.5 acres
Problem 10: Square feet to square yards
\(1\text{ yd}=3\text{ ft}\), so \(1\text{ yd}^{2}=9\text{ ft}^{2}\).
\(540\text{ ft}^{2}\times \frac{1\text{ yd}^{2}}{9\text{ ft}^{2}}=60\text{ yd}^{2}\).
60 yd2
Algebra 1 Units Worksheet Answer Key: problems 11–15
Problem 11: Reading a measurement
The ruler is accurate to the nearest tenth, so the true length is within half a tenth, \(0.05\text{ in}\), of \(3.4\).
\(3.4-0.05\le L< 3.4+0.05\).
\(3.35\le L< 3.45\)
Problem 12: Choosing a vertical scale
Data range: \(340-310=30\).
Graph A: axis height \(400-0=400\), and \(\frac{30}{400}=0.075=7.5\%\).
Graph B: axis height \(350-300=50\), and \(\frac{30}{50}=0.6=60\%\).
Graph A: 7.5%. Graph B: 60%. Graph B shows the changes much more clearly.
Problem 13: Choosing an origin
(a) \(2026-2010=16\), so \(x=16\).
(b) \(P\) is in thousands: \(48.3\times 1000=48{,}300\). The population is 48,300 people.
(c) \(2010+22=2032\). 2032
Problem 14: Defining a quantity
Let \(h\) be the rental time in hours and \(C\) the total cost in dollars. The equation is \(C=8+12h\).
For \(h=3\): \(C=8+36=44\). For \(C=80\): \(12h=72\), so \(h=6\).
\(\$44\) for 3 hours; 6 hours for \(\$80\)
Problem 15: Rounding a product
Each measurement has two significant digits, so the area should not show more than two: \(35.04\approx 35\).
About \(35\text{ in}^{2}\)
Algebra 1 Units Worksheet Answer Key: problems 16–20
Problem 16: Units of a slope
(a) Use \((0,0)\) and \((2,110)\): \(\frac{110-0}{2-0}=55\).
(b) Slope units are \(\frac{\text{miles}}{\text{hours}}\): the truck travels \(55\) miles per hour.
(c) \(d=55\times 3.5=192.5\).
(a) 55 (b) 55 mi/h (c) 192.5 mi
Problem 17: Gallons in a tank
Volume: \(4\times 3\times 2=24\text{ ft}^{3}\).
\(24\text{ ft}^{3}\times \frac{7.48\text{ gal}}{1\text{ ft}^{3}}=179.52\text{ gal}\).
About 179.5 gallons
Problem 18: Percent error of a length
The greatest error is half of the smallest division: \(0.05\text{ ft}\).
\(\frac{0.05}{12.5}=0.004=0.4\%\).
\(0.05\text{ ft}\), or \(0.4\%\)
Problem 19: Speed of sound
\(1125\,\frac{\text{ft}}{\text{s}}\times \frac{1\text{ mi}}{5280\text{ ft}}\times \frac{3600\text{ s}}{1\text{ h}}=\frac{4{,}050{,}000}{5280}\,\frac{\text{mi}}{\text{h}}\approx 767.05\,\frac{\text{mi}}{\text{h}}\).
About 767 mi/h
Problem 20: Walking time
\(8\text{ mi}\times \frac{1\text{ h}}{3.2\text{ mi}}=2.5\text{ h}\).
\(0.5\text{ h}=30\text{ min}\).
2.5 h, or 2 h 30 min
Algebra 1 Units Worksheet Answer Key: problems 21–23
Problem 21: Filling the gas tank
(a) \(12\text{ gal}\times \frac{\$3.80}{1\text{ gal}}=\$45.60\).
(b) \(12\text{ gal}\times \frac{32\text{ mi}}{1\text{ gal}}=384\text{ mi}\).
(c) \(100\text{ mi}\times \frac{1\text{ gal}}{32\text{ mi}}\times \frac{\$3.80}{1\text{ gal}}=\$11.875\approx\$11.88\).
(a) \(\$45.60\) (b) 384 mi (c) \(\$11.88\)
Problem 22: Filling a pool
Time: \(6000\text{ gal}\times \frac{1\text{ min}}{12\text{ gal}}=500\text{ min}\). \(500=8\times 60+20\), so 8 h 20 min.
Cost: \(6\times \$4.50=\$27.00\).
8 h 20 min; \(\$27.00\)
Problem 23: Printing a packet
Time: \(2700\text{ pages}\times \frac{1\text{ min}}{18\text{ pages}}=150\text{ min}=2.5\text{ h}\).
Sheets: \(2700: 2=1350\). Reams: \(1350: 500=2.7\), so Noah must buy \(3\) whole reams.
Cost: \(3\times \$6.25=\$18.75\).
2.5 hours; \(\$18.75\)
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Algebra 1 Units, Quantities and Modeling worksheet answer key
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