a. Answer The given information is not enough to determine the cost of 1 gallon of gasoline and 1 quart of oil. Explanation Given information: Cost of 10 gallons of gasoline and 2 quarts of oil is $45.50 and cost of 5 gallons of gasoline and 1 quarts of oil is $22.75. Calculation: Let a be the cost of 1 gallon of gasoline and b be the cost of 1 quart of oil. So using above given information we can write 2 equations 10 a + 2 b = 45.50... ( i ) 5 a + b = 22.75... ( i i ) Now dividing equation (i) by 2, we get 5 a + b = 22.75... ( i i i ) Now we can see that equation (ii) and (iii) are same, it means we can say that we are not given 2 different equations ,we are given 1 equation with two variables. Therefore we cannot find the values of variables. Conclusion: The given information is not enough to determine the costs. b. To determine To calculate: You pay $45.50 for 10 gallons of gasoline and 2 quarts of oil at a gas station. Your friend pays $22.75 for 5 gallons of the same gasoline and 1 quart of the same oil. The receipt shown is for buying the same gasoline and same oil. Is there now enough information to determine the cost of 1 gallon of gasoline and 1 quart of oil? Explain. Answer Yes, we can find the cost of 1 gallon and 1 qart. Explanation Given information: Cost of 10 gallons of gasoline and 2 quarts of oil is $45.50 and cost of 8 gallons of gasoline and 2 quarts of oil is $38.45. Calculation: Let a be the cost of 1 gallon of gasoline and b be the cost of 1 quart of oil. So using above given information we can write 2 equations 8 a + 2 b = 38.45... ( i v ) 10 a + 2 b = 45.50... ( v ) Here from equation (iv) and (v) we can say that we have 2 different equations with 2 variables, So we can find the value of both variables. Conclusion: We can determine the costs. c. To determine To calculate : You pay $45.50 for 10 gallons of gasoline and 2 quarts of oil at a gas station. Your friend pays $22.75 for 5 gallons of the same gasoline and 1 quart of the same oil. Determine the cost of 1 gallon of gasoline and 1 quart of oil. Answer Cost of 1 gallon of gasoline is $3.55 and cost of 1 quart of oil is $5. Explanation Given information: From the above part we have 8 a + 2 b = 38.45... ( i v ) 10 a + 2 b = 45.50... ( v ) Calculation: Subtracting equation (iv) from (v), we get ( 10 − 8 ) a = 45.50 − 38.45 2 a = 7.1 → a = 3.55 Now putting value of a in equation (v), we get 8 * 3.55 + 2 b = 38.40 2 b = 10 ⇒ b = 5 Conclusion: The cost of 1 gallon of gasoline is $3.55 and cost of 1 quart of oil is $5.

Big Ideas Math A Bridge To Success Algebra 1: Student Edition 2015

1st Edition

ISBN: 9781680331141

Author: HOUGHTON MIFFLIN HARCOURT

Publisher: Houghton Mifflin Harcourt

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Question

Chapter 5, Problem 12CT

To determine

To check: Is there enough information to determine the cost of 1 gallon of gasoline and 1 quart of oil.Explain.

Expert Solution

Answer to Problem 12CT

The given information is not enough to determine the cost of 1 gallon of gasoline and 1 quart of oil.

Explanation of Solution

Given information: Cost of 10 gallons of gasoline and 2 quarts of oil is $45.50 and cost of 5 gallons of gasoline and 1 quarts of oil is $22.75.

Calculation: Let a be the cost of 1 gallon of gasoline and b be the cost of 1 quart of oil.

So using above given information we can write 2 equations

10a+2b=45.50...(i)

5a+b=22.75...(ii)

Now dividing equation (i) by 2, we get

5a+b=22.75...(iii)

Now we can see that equation (ii) and (iii) are same, it means we can say that we are not given 2 different equations ,we are given 1 equation with two variables. Therefore we cannot find the values of variables.

Conclusion: The given information is not enough to determine the costs.

To determine

To calculate: You pay $45.50 for 10 gallons of gasoline and 2 quarts of oil at a gas station. Your friend pays $22.75 for 5 gallons of the same gasoline and 1 quart of the same oil. The receipt shown is for buying the same gasoline and same oil. Is there now enough information to determine the cost of 1 gallon of gasoline and 1 quart of oil? Explain.

Expert Solution

Answer to Problem 12CT

Yes, we can find the cost of 1 gallon and 1 qart.

Explanation of Solution

Given information: Cost of 10 gallons of gasoline and 2 quarts of oil is $45.50 and cost of 8 gallons of gasoline and 2 quarts of oil is $38.45.

Calculation: Let a be the cost of 1 gallon of gasoline and b be the cost of 1 quart of oil.

So using above given information we can write 2 equations

8a+2b=38.45...(iv)

10a+2b=45.50...(v)

Here from equation (iv) and (v) we can say that we have 2 different equations with 2 variables, So we can find the value of both variables.

Conclusion: We can determine the costs.

To determine

To calculate: You pay $45.50 for 10 gallons of gasoline and 2 quarts of oil at a gas station. Your friend pays $22.75 for 5 gallons of the same gasoline and 1 quart of the same oil. Determine the cost of 1 gallon of gasoline and 1 quart of oil.

Expert Solution

Answer to Problem 12CT

Cost of 1 gallon of gasoline is $3.55 and cost of 1 quart of oil is $5.

Explanation of Solution

Given information: From the above part we have

8a+2b=38.45...(iv)

10a+2b=45.50...(v)

Calculation: Subtracting equation (iv) from (v), we get

(10−8)a=45.50−38.45

2a=7.1 → a=3.55

Now putting value of a in equation (v), we get

8*3.55+2b=38.40

2b=10 ⇒ b=5

Conclusion: The cost of 1 gallon of gasoline is $3.55 and cost of 1 quart of oil is $5.

Chapter 5, Problem 11CT

Chapter 5, Problem 13CT

Chapter 5 Solutions

Big Ideas Math A Bridge To Success Algebra 1: Student Edition 2015

Ch. 5.1 - Prob. 1E Ch. 5.1 - Prob. 2E Ch. 5.1 - Prob. 3E Ch. 5.1 - Prob. 4E Ch. 5.1 - Prob. 5E Ch. 5.1 - Prob. 6E Ch. 5.1 - Prob. 7E Ch. 5.1 - Prob. 8E Ch. 5.1 - Prob. 9E Ch. 5.1 - Prob. 10E

Ch. 5.1 - Prob. 11E Ch. 5.1 - Prob. 12E Ch. 5.1 - Prob. 13E Ch. 5.1 - Prob. 14E Ch. 5.1 - Prob. 15E Ch. 5.1 - Prob. 16E Ch. 5.1 - Prob. 17E Ch. 5.1 - Prob. 18E Ch. 5.1 - Prob. 19E Ch. 5.1 - Prob. 20E Ch. 5.1 - Prob. 21E Ch. 5.1 - Prob. 22E Ch. 5.1 - Prob. 23E Ch. 5.1 - Prob. 24E Ch. 5.1 - Prob. 25E Ch. 5.1 - Prob. 26E Ch. 5.1 - Prob. 27E Ch. 5.1 - Prob. 28E Ch. 5.1 - Prob. 29E Ch. 5.1 - Prob. 30E Ch. 5.1 - Prob. 31E Ch. 5.1 - Prob. 32E Ch. 5.1 - Prob. 33E Ch. 5.1 - Prob. 34E Ch. 5.1 - Prob. 35E Ch. 5.1 - Prob. 36E Ch. 5.2 - Prob. 1E Ch. 5.2 - Prob. 2E Ch. 5.2 - Prob. 3E Ch. 5.2 - Prob. 4E Ch. 5.2 - Prob. 5E Ch. 5.2 - Prob. 6E Ch. 5.2 - Prob. 7E Ch. 5.2 - Prob. 8E Ch. 5.2 - Prob. 9E Ch. 5.2 - Prob. 10E Ch. 5.2 - Prob. 11E Ch. 5.2 - Prob. 12E Ch. 5.2 - Prob. 13E Ch. 5.2 - Prob. 14E Ch. 5.2 - Prob. 15E Ch. 5.2 - Prob. 16E Ch. 5.2 - Prob. 17E Ch. 5.2 - Prob. 18E Ch. 5.2 - Prob. 19E Ch. 5.2 - Prob. 20E Ch. 5.2 - Prob. 21E Ch. 5.2 - Prob. 22E Ch. 5.2 - Prob. 23E Ch. 5.2 - Prob. 24E Ch. 5.2 - 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Prob. 49E Ch. 5.7 - Prob. 50E Ch. 5.7 - Prob. 51E Ch. 5.7 - Prob. 52E Ch. 5.7 - Prob. 53E Ch. 5.7 - Prob. 54E Ch. 5.7 - Prob. 55E Ch. 5 - Prob. 1CR Ch. 5 - Prob. 2CR Ch. 5 - Prob. 3CR Ch. 5 - Prob. 4CR Ch. 5 - Prob. 5CR Ch. 5 - Prob. 6CR Ch. 5 - Prob. 7CR Ch. 5 - Prob. 8CR Ch. 5 - Prob. 9CR Ch. 5 - Prob. 10CR Ch. 5 - Prob. 11CR Ch. 5 - Prob. 12CR Ch. 5 - Prob. 13CR Ch. 5 - Prob. 14CR Ch. 5 - Prob. 15CR Ch. 5 - Prob. 16CR Ch. 5 - Prob. 17CR Ch. 5 - Prob. 18CR Ch. 5 - Prob. 19CR Ch. 5 - Prob. 20CR Ch. 5 - Prob. 21CR Ch. 5 - Prob. 22CR Ch. 5 - Prob. 1CT Ch. 5 - Prob. 2CT Ch. 5 - Prob. 3CT Ch. 5 - Prob. 4CT Ch. 5 - Prob. 5CT Ch. 5 - Prob. 6CT Ch. 5 - Prob. 7CT Ch. 5 - Prob. 8CT Ch. 5 - Prob. 9CT Ch. 5 - Prob. 10CT Ch. 5 - Prob. 11CT Ch. 5 - Prob. 12CT Ch. 5 - Prob. 13CT Ch. 5 - Prob. 14CT Ch. 5 - Prob. 15CT Ch. 5 - Prob. 1CA Ch. 5 - Prob. 2CA Ch. 5 - Prob. 3CA Ch. 5 - Prob. 4CA Ch. 5 - Prob. 5CA Ch. 5 - Prob. 6CA Ch. 5 - Prob. 7CA Ch. 5 - Prob. 8CA Ch. 5 - Prob. 9CA Ch. 5 - Prob. 10CA

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