Algebra Question?

Could someone please show me how to solve the following problem?

A grocery store sells bananas for $0.50 each and oranges for $0.80 each.  If a bag of bananas and oranges costs $11.90, and there were a total of 19 bananas and oranges, how many oranges were purchased?

a. 7

b. 8

c. 10

d. 11

e. 12

I appreciate your time and help.  

8 Answers

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  • 2 months ago
    Favorite Answer

    It is a pleasure to help someone who uses super manners and words like 'please' and 'appreciate'...please spread to the rest of humankind!!

    Anyway, we can set up the following equations.

    0.5b + 0.8o = 11.9...(1)

    b + o = 19...(2)

    From (2) we have:

    o = 19 - b

    so, into (1) for o gives:

    0.5b + 0.8(19 - b) = 11.9

    so, 15.2 - 0.3b = 11.9

    i.e. 0.3b = 3.3

    => b = 11

    Hence, o = 19 - 11 => 8

    Therefore, 11 bananas and 8 oranges

    :)>

  • 2 months ago

    the bag of oranges and bananas cost 11.90 -- 19 bananas cost 9.50, so the oranges must have cost 2.40 (11.90 - 9.50). Since oranges cost 80 cents each, and the total number of oranges in the bag cost 2.40, that means the number or oranges in the bag is $2.40 / $0.80 = 3 oranges. 

  • 2 months ago

    let x = bananas , y - oranges

    0.50x + 0.80y = 11.90 eq1

      0.80[x + y = 19] eq2

    ---------------------------

    0.50x + 0.80y = 11.90

    -[ 0.80x + 0.80y = 15.2]

    ---------------------------------

    .........-0.3x = -3.3

    .............x = 11

    solving for y from eq2

    x + y = 19

    11 + y = 19

    y = 19 - 11

    y = 8

    Therefore, there are 8 oranges that are purchase..

    Answer is b. 8

  • 2 months ago

    .5x+.8y=11.90

    x=19-y

    5x+8y=119

    5(19-y)+8y=119

    95-5y+8y=119

    3y=119-95=24>>y=8bananas

    19-8=11oranges

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  • 2 months ago

    Let B=the number of bananas; O=the number of oranges.

    0.5B+0.8O=11.9

    B+O=19

    =>

    0.5(19-O)+0.8O=11.9

    =>

    0.3O=11.9-9.5

    =>

    0.3O=2.4

    =>

    O=8 (b)

  • Jeremy
    Lv 6
    2 months ago

    B = numbers of bananas that were purchased 

    O = numbers of oranges that were purchased

    SYSTEM:

    {B + O = 19

    {0.50 * B + 0.80 * O = 11.90

    B = 19 - O <=== Plug this expression into the second equation. 

    0.50 * (19 - O) + 0.80 * O = 11.90 ==> 9.50 - 0.50 * O + 0.80 * O = 11.90 ==>

    ==> 9.50 + 0.30 * O = 11.90 ==> 0.30 * O = 11.90 - 9.50 ==> 0.30 * O = 2.40 ==>

    ==> O = 2.40 / 0.30 ==> O = 8

    ANSWER: 8 oranges (and 11 bananas) 

  • 2 months ago

    This is a classic type of problem that can be solved with algebra, or without.

    With algebra, the usual idea is to give variable names to the numbers you want to find, write down equations from the statements in the problem, and then solve those equations.  Suppose there are x oranges and y bananas.  Then the problem statements can be written as:

        x + y = 19                 "a total of 19 oranges and bananas in the bag"

        0.5x + 0.8y = 11.90   "total cost of the oranges and bananas"

    That's a system of equations and you'd typically use either elimination or substitution to solve.  You really only need the value of x.

    But with some arithmetic and common sense, you can get the answer more directly.  You know that 19 oranges cost 19*0.50 = $9.50.  Replace an orange with a banana in the bag and the cost increases by 0.80 - 0.50 = 0.30, or thirty cents.  How many times to you need to do that to get the total up to 11.90?  Take the difference (11.90 - 9.50 = 2.40) and divide by the 0.30 extra cost per banana and you get 2.4/0.3 = 8 bananas.  So, there must have been 11 oranges to make 19 fruits in all.

    Is that right?  Check the answer to be sure:

    11 oranges at 0.50 each cost 11*0.50 = $5.50

    8 bananas at 0.80 each cost 8*0.80 = $6.40

    Total cost is $5.50 + $6.40 = $11.90

  • david
    Lv 7
    2 months ago

    b + o = 19

    0.50b + 0.80o  =  11.90  >>>  multiply by 2

    b + 1.60o = 23.80   .....  subtract top equation

    -b  -o  =  -19

     0,60o = 4.80

       o  =  8  oranges

       b = 19 - o  =  11 bananas

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