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Math Help - Let x= the unknown.

  1. #1
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    Let x= the unknown.

    1. If a car traveled 452 miles on 13 gallons of gas, how many miles per gallon did the car average on the
    trip?
    a. 452x = 13
    b. 452 = x 13
    c. 13x = 452
    d. 13 + x = 452

    2. The product of two numbers is 1692. If the smaller number is 730 less than the larger number, find
    the larger number.
    a. x(x 730) = 1692
    b. x(730 x) = 1692
    c. 730x = x 1692
    d. x + x 730 = 1692

    3. An appliance repairman charges $60 for a house call, and $30 per hour for labor. How many hours is
    the repairman estimating to work at your home if the quote for the total price is $127.50 and there is
    no charge for parts?
    a. 30x 60 = 127.50
    b. 30x + 60 = 127.50
    c. 30 + 60x = 127.50
    d. 30x 127.60 = 60

    4. Victor bought 5 posters on sale. The original cost of all 5 posters was $73.25, but she only paid $51.89
    for all 5 posters. How much did she save on each poster?
    a. 51.89 / (5x) = 73.25
    b. 73.25 51.89 = 5x
    c. 73.25 / 5 = 51.89x
    d. 73.25 51.89 = x

    5. 35. Because of a flu epidemic, of all students were absent from school. If 156 students were absent,how many students are enrolled in the school?
    a. 1/12x x = 156
    b. 11/12x x = 156
    c. 1/12x x = 156
    d. 11/12x x =156


    Alright, these problems are on a practice exam and no matter how much I read about them in the lesson, I just cant seam to get my head around any of these. Could someone dumb it down for me?
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  2. #2
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    Quote Originally Posted by ChristieZissler View Post
    5. 35. Because of a flu epidemic, of all students were absent from school. If 156 students were absent,how many students are enrolled in the school?
    a. 1/12x x = 156
    b. 11/12x x = 156
    c. 1/12x x = 156
    d. 11/12x x =156
    First of all, number 5 needs some fixing. I dont think the problem is there all the way. And, i don't know about number 4.....

    anways...

    1. If a car traveled 452 miles on 13 gallons of gas, how many miles per gallon did the car average on the
    trip?
    a. 452x = 13
    b. 452 = x 13
    c. 13x = 452
    d. 13 + x = 452
    So (my explanations suck, so bear with me on this), a car travels 452 miles--that is considered the "independent variable" i think, meaning, you cant do anything to that number. You just kind of leave it alone. You are trying to find how many miles per gallon. That tells you what the equation is. so the equation would be "13x = 452." See you are trying to find how many miles per gallon, and they give you the number of gallons (13) you used....oh geez, it's so hard to explain....i'm sorry.

    2. The product of two numbers is 1692. If the smaller number is 730 less than the larger number, find
    the larger number.
    a. x(x 730) = 1692
    b. x(730 x) = 1692
    c. 730x = x 1692
    d. x + x 730 = 1692
    Okay, so this one is saying there are two numbers, when multiplied together, you get 1692. So, one number will he called "x" the other, lets say, is "y." You're equation thus far would be xy=1692 okay? but they give you more...
    Your smaller number ("y") is 730 less than the larger number ("x"). You would just substitute "y" for x-730, right? so your equation would be x(x-730) = 1692 which is A....

    3. An appliance repairman charges $60 for a house call, and $30 per hour for labor. How many hours is
    the repairman estimating to work at your home if the quote for the total price is $127.50 and there is
    no charge for parts?
    a. 30x 60 = 127.50
    b. 30x + 60 = 127.50
    c. 30 + 60x = 127.50
    d. 30x 127.60 = 60
    Okay, so the repairman charges $60 just for calling. So you are automatically paying $60 bucks. The repairman also charges $30 for every hour he works. So, if "x" is the number of hours he works, then it would be "30x" in his case...

    You end up paying $127.50 after he's done. how many hours did this guy work? So, you know he charges $30 dollars per hour, so your equation would be 30x = 127.50 BUT he also charged that $60 dollars just for calling, so it would be 30x + 60 = 127.50 which is B.

    Sorry for the sucky explanations. I bet someone can explain it better... Hope i helped though!
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  3. #3
    MHF Contributor Reckoner's Avatar
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    Hi, ChristieZissler. blair_alane's explanations for 2 and 3 are good. Problem 5 was not stated properly, and for the rest:

    Quote Originally Posted by ChristieZissler View Post
    1. If a car traveled 452 miles on 13 gallons of gas, how many miles per gallon did the car average on the
    trip?
    a. 452x = 13
    b. 452 = x 13
    c. 13x = 452
    d. 13 + x = 452
    On average, the car travels 452 miles for every 13 gallons of gas. This means the car gets 452 miles per 13 gallons, so the car's mileage per gallon is \frac{452}{13}. If we let x be the number of miles per gallon that the car gets, we have

    x = \frac{452}{13}\Rightarrow{\color{red}13\ \cdot\ }x = \frac{452\color{red}\cdot13}{13}\Rightarrow 13x = 452

    Quote Originally Posted by ChristieZissler View Post
    4. Victor bought 5 posters on sale. The original cost of all 5 posters was $73.25, but she only paid $51.89
    for all 5 posters. How much did she save on each poster?
    a. 51.89 / (5x) = 73.25
    b. 73.25 51.89 = 5x
    c. 73.25 / 5 = 51.89x
    d. 73.25 51.89 = x
    Victor saves x dollars on every poster. But there are 5 posters, so her total savings are 5\cdot x = 5x. But we know that she saves a total of 73.25 - 51.89 dollars. Now, just equate these two expressions.

    Quote Originally Posted by blair_alane View Post
    a car travels 452 miles--that is considered the "independent variable" i think, meaning, you cant do anything to that number
    452 is a constant, not a variable. An independent variable refers to an input of a function, or in other words, a value that you can manipulate to produce a change in a dependent variable. If the mileage per gallon were expressed as a function of the number of miles traveled (e.g. y = x / 13), then the variable representing the number of miles would be the independent variable.
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  4. #4
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    Quote Originally Posted by Reckoner View Post
    452 is a constant, not a variable. An independent variable refers to an input of a function, or in other words, a value that you can manipulate to produce a change in a dependent variable. If the mileage per gallon were expressed as a function of the number of miles traveled (e.g. y = x / 13), then the variable representing the number of miles would be the independent variable.
    Heehee! Aahhh....I see! Thank you SO SO much, Reckoner!

    By the way, you explain things SO much better than I do! I started to confuse myself! Thank you!
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