Algebra Problem: multiple variables?

For a wedding, Shered bought several dozen roses and several dozen carnations. The roses cost $15 per dozen, and the carnations cost $8 per dozen. Shered bought a total of 17 dozen flowers and paid a total of $192. How many roses did she buy?

Could you PLEASE explain step by step, I know this is basic algebra lol but I forgot..thanks (:

Comments

  • we have two equations: r = roses c= carnations

    1) r + c = 17

    2) 15r + 8c = 192

    Use substitution: so take equation 1 subtract r from both sides and make it

    c = 17 - r Now sub it into equation 2

    15r + 8(17-r) = 192

    15r + 136 - 8r = 192

    7r + 136 = 192 subtract 136 from both sides

    7r = 56 divide by 7

    r = 8 now use r = 8 in equation 1

    8 + c = 17

    c = 9

    so you will have 8 dozen roses and 9 dozen carnations

    i am glade to help u :) :) :) :)

  • roses = x

    carnations = y

    You have two equations that "stem" (see what I did there?) from the information above. the first equation at the bottom of this paragraph correlates to the amount of money that Shered bought. She bought an X amount of roses at $15 a dozen, and a Y amount of carnations at $8 a dozen for a total of $192.

    The second equation says that Shered bought an X amount of roses and a Y amount of carnations for a grand total of 17 dozens total.

    1. 192 = 15x + 8y

    2. 17 = x + y

    17 - x = y <----- isolate your y-variable. Now that you have an equation that equals y, you can plug this into your first equation.

    192 = 15x + 8(17 - x)

    distribute.

    192 = 15x + 136 - 8x

    combine like terms

    192 = 7x + 136

    7x = 192 - 136

    7x = 56

    x = 8

    Shered bought 8 dozen roses

    Hope that helps!

  • r + c = 17

    15 r + 8 c = 192

    multiply eqn 1 by 8

    8 r + 8 c = 136

    subtract from eqn 2

    7r = 56

    r = 8

    c = 9

  • No. Dozen Roses = r

    No. Dozen Carnations = c

    r + c = 17

    c = 17 - r ............... Eq. 1

    15r + 8c = 192 .... Eq. 2

    Sub 17 - r from Eq. 1 for c in Eq. 2:

    15r + 8(17 - r) = 192

    15r + 136 - 8r = 192

    7r = 192 - 136

    7r = 56

    r = 56 / 7

    r = 8

    Shered bought 8 doz. roses, or 96 roses.

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  • x + y = 17

    15x + 8y = 192

    - 8x - 8y = - 136

    15x + 8y = 192

    7x = 56

    x = 8 and y = 9

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