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

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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

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• 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

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• 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.

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