Julia sells plants for $12 each and flowers at $2 each. Let x be the number of plants.
Part a) if she sold 3 flowers more than twice the number of plants, write an algebraic expression to represent the number of flowers.
Part b) if she collected $870, how many plants did she sell?
Part c) how many flowers did she sell
husoski
Favorite Answer
This is a good example of how algebra is easier than English.
"3 flowers more than twice the number of plants" = 2x + 3
The expression on the right is obvious. Take whatever x is, multiply by 2 and then add 3. The phrase on the left takes a little more thought, but gets to the same place.
That's the number of flowers sold. Call it y, so that:
y = 2x + 3
If Julia sells x plants and y flowers, then her gross receipts (call that R) in dollars come to:
R = 12x + 2y
Starting here, the algebra requires a bit of pencil work. Start by substituting (2x + 3) for y so that x is the only variable on the right; then simplify:
R = 12x + 2(2x + 3)
R = 12x + 4x + 6 . . . . distributive property
R = 16x + 6 . . . . combine like terms
But R=870 was given, so if you substitute that you get a simple two-step equation:
16x + 6 = 870
16x = 864
x = 864/16 = 54
?
a) y = number of flowers sold
y = 2x+3
b) 870 = 12x+2(2x+3) =16x+6
16x = 864
x = 54 plants
c) y = 111 flowers
derfram
x = number of plants sold
2x + 3 = number of flowers sold
12x = income from plant sales
2(2x + 3) = 4x + 6 = income from flower sales
a) Number of flowers sold 2x + 3.
b)Income from plants + income from flowers = 870, so:
12x + 4x + 6 = 870
16x + 6 = 870
16x = 864
x = 864/16 = 54
So she sold 54 plants.
c) number of flowers sold 2x + 3 = 2*54 + 3 = 111 flowers.