**Comparing Rates :**

In this section, you will learn, how to compare the given two measures by converting them into unit rates.

**Example :**

Compare "8 dolls cost $120" and "6 dolls cost $102".

To compare the given measures, convert than in to unit rates.

Cost of 1 doll = 120 / 8 Cost of 1 doll = $ 15 |
Cost of 1 doll = 102 / 6 Cost of 1 doll = $ 17 |

" 8 dolls cost $120" is less than "6 dolls cost $102"

Because, unit rate in "8 dolls cost $120" is $15. But the unit rate in "6 dolls cost $102" is $17.

**Problem 1 :**

Which is best,

10 pencils cost $4

or

6 pencils cost $2.70 ?

**Solution : **

To compare the given measures, convert them in to unit rates.

Cost of 10 pencils = $4 Cost of 1 pencil = 4/10 Cost of 1 pencil = $0.40 |
Cost of 6 pencils = $2.70 Cost of 1 pencil = 2.7/6 Cost of 1 pencil = $0.45 |

We get the lowest price per pencil $0.40 in "10 pencils cost $4"

Hence, "10 pencils cost $4" is the best deal.

**Problem 2 :**

Which is best,

2 liters of milk at $3.80

or

1.5 liters of milk at $2.70 ?

**Solution : **

**To compare the given measures, convert them in to unit rates. **

2 liters of milk at $3.80 Cost of 1 liter = 3.8/2 Cost of 1 liter = $1.90 |
2 liters of milk at $2.70 Cost of 1 liter = 2.7/1.5 Cost of 1 liter = $1.8 |

From the above unit rates, we get the lower price per liter of milk $1.8 in "2 liters cost $2.70"

Hence, "2 liters cost $2.70" is the best deal.

**Problem 3 :**

Who is better in earning,

David earns $57.60 in 8 hours

or

John earns $90 in 12 hours ?

**Solution : **

**To compare the given measures, convert them in to unit rates. **

Earning in 8 hrs = $57.60 Earning in 1 hr = 57.60/8 Earning in 1 hr = $7.20 |
Earning in 12 hrs = $90 Earning in 1 hr = 90/12 Earning in 1 hr = $7.50 |

From the above unit rates, John earns more than David per hour.

Hence, John is earning better.

**Problem 4 :**

Who is driving faster,

Alex covers 120 miles in 3 hours

or

Jose covers 84 miles in 2 hours ?

**Solution : **

**To compare the given measures, convert them in to unit rates. **

Distance in 3 hrs = 120 miles Distance in 1 hr = 120/3 Distance in 1 hr = 40 miles |
Distance in 2 hrs = 84 miles Distance in 1 hr = 84/2 Distance in 1 hr = 42 miles |

From the above unit rates, Jose covers more miles than David per hour.

Hence, Jose is driving faster.

**Problem 5 :**

Who is better,

Lily can prepare 10.4 gallons of juice in 4 days

or

Rosy can prepare 7.5 gallons of juice in 3 days ?

**Solution : **

**To compare the given measures, convert them in to unit rates. **

No.gallons in 2 days = 5.2 No.of gallons in 1 day = 5.2/2 No.of gallons in 1 day = 2.6 |
No. gallons in 3 days = 7.5 No. of gallons in 1 day = 7.5/3 No.of gallons in 1 day = 2.5 |

From the above unit rates, Lily prepares more gallons than day.

Hence, Lily is better.

**Problem 6 :**

Which is best,

500 grams cheese cost $ 3.25

or

1.5 kilograms cheese cost $ 9.9

**Solution : **

**To compare the given measures, convert them in to unit rates in price per kilogram. **

500 grams -----> $3.25 1 kilogram = 2 ⋅ 500 grams Price of 1 kg = 2 ⋅ 3.25 Price of 1 kg = $6.5 |
1.5 kilograms -----> $9.9 Price of 1 kg = 9.9 / 1.5 Price of 1 kg = $6.6 |

From the above unit rates, we get the lower price per kilogram $6.5 in "500 grams cheese cost $ 3.25"

Hence, "500 grams cheese cost $ 3.25" is the best deal.

**Problem 7 :**

Who is driving faster,

Lenin covers 6 miles in 2 minutes

or

Daniel covers 225 miles in 1.5 hours ?

**Solution : **

**To compare the given measures, convert them in to unit rates in distance per hour. **

Distance in 2 min = 6 miles Distance in 1 min = 3 miles 1 hour = 60 minutes Distance in 1 hr = 60 ⋅ 3 Distance in 1 hr = 180 miles |
Distance in 1.5 hrs = 225 miles Distance in 1 hr = 225 / 1.5 Distance in 1 hr = 150 miles |

From the above unit rates, Lenin covers more miles than Daniel per hour.

Hence, Lenin is driving faster.

**Problem 8 :**

Who is better in walking,

Shanel walks 2/ 5 of a mile every 1/7 hour.

or

Declan walks 3/5 of a mile every 2/7 hour ?

**Solution : **

**To compare the given measures, convert them in to unit rates in miles per hour (speed).**

**Speed = Distance / Time **

Speed = (2/5) / (1/7) Speed = (2/5) ⋅ (7/1) Speed = 14 / 5 Speed = 2.8 miles per hour |
Speed = (3/5) / (2/7) Speed = (3/5) ⋅ (7/2) Speed = 21 / 10 Speed = 2.1 miles per hour |

From the above unit rates, Shanel walk more miles than Declan per hour.

Hence, Shanel is better in walking.

**Problem 9 :**

Who is better,

Daniel answered 240 answers correctly out of 300 questions

or

Deborah answered 328 questions correctly out of 400 questions ?

**Solution : **

**To compare the given measures, convert them in to percentages .**

**Percent is **

** = [no. of correct answers/ Total no. of questions] x 100 % **

Percent = [240/300] ⋅ 100 % Percent = 80 % |
Percent = [328/400] ⋅ 100 % Percent = 82 % |

From the above percentages, Deborah answered more questions correctly than Daniel per 100.

Hence, Deborah is better.

**Problem 10 :**

Which is best,

Plan A : Income of $250 on $5000 investment

or

Plan B : Income of $280 on $7000 investment

**Solution : **

**To compare the given measures, convert them in to percentages of income .**

**Percent of income = [Income / Investment] x 100 % **

Percent = [250/5000] ⋅ 100% Percent of income = 5 % |
Percent = [280/7000] ⋅ 100% Percent of income = 4 % |

From the above percentages, plan A gives more income than plan B per $100 investment.

Hence, plan A is better.

After having gone through the stuff given above, we hope that the students would have understood how to solve problems by comparing unit rates.

Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.

Widget is loading comments...

You can also visit our following web pages on different stuff in math.

**WORD PROBLEMS**

**Word problems on simple equations **

**Word problems on linear equations **

**Word problems on quadratic equations**

**Area and perimeter word problems**

**Word problems on direct variation and inverse variation **

**Word problems on comparing rates**

**Converting customary units word problems **

**Converting metric units word problems**

**Word problems on simple interest**

**Word problems on compound interest**

**Word problems on types of angles **

**Complementary and supplementary angles word problems**

**Trigonometry word problems**

**Markup and markdown word problems **

**Word problems on mixed fractrions**

**One step equation word problems**

**Linear inequalities word problems**

**Ratio and proportion word problems**

**Word problems on sets and venn diagrams**

**Pythagorean theorem word problems**

**Percent of a number word problems**

**Word problems on constant speed**

**Word problems on average speed **

**Word problems on sum of the angles of a triangle is 180 degree**

**OTHER TOPICS **

**Time, speed and distance shortcuts**

**Ratio and proportion shortcuts**

**Domain and range of rational functions**

**Domain and range of rational functions with holes**

**Graphing rational functions with holes**

**Converting repeating decimals in to fractions**

**Decimal representation of rational numbers**

**Finding square root using long division**

**L.C.M method to solve time and work problems**

**Translating the word problems in to algebraic expressions**

**Remainder when 2 power 256 is divided by 17**

**Remainder when 17 power 23 is divided by 16**

**Sum of all three digit numbers divisible by 6**

**Sum of all three digit numbers divisible by 7**

**Sum of all three digit numbers divisible by 8**

**Sum of all three digit numbers formed using 1, 3, 4**

**Sum of all three four digit numbers formed with non zero digits**

**Sum of all three four digit numbers formed using 0, 1, 2, 3**

**Sum of all three four digit numbers formed using 1, 2, 5, 6**

HTML Comment Box is loading comments...