Hi, Marina. Here's how you can solve problems like these:

Read the problem, and identify the question:

We have 302 flowers and will be making 112 corsages, some carnations, which use 3 flowers each, and roses, which use 2 flowers each.

Ask the Question: How many of each type of corsage did the florist make.

Now we identify the unknowns, which we will call the variables:

We'll let C be the # of carnations corsages made, and R the # of rose corsages.

Now, we write down expressions that put into math language (Equations or Eq for short) what we know:

(1) C+R = 112 --------------> This formula is easy

(2) 3C + 2R = 302 --------------> This expression "says" that of the 302 flowers

the carnations use 3 flowers and the roses use 2.

So now we have two equations (Eq 1 and Eq 2) and two unknowns, so we solve them this way:

Use Eq. 1 to solve for C in relationship to R. As a result, Eq. 1 is now:

(1) C=112-R

Now we take Eq 2 and replace the variable C with **R + 112**

2) 3(112-R) + 2R = 302 -----------------> Now we do the simple part. We solve for R:

-3R + 3*112 + 2R = 302 -----------------> multiply 3 by 112 and -R, and re-write the Eq.

336 -3R+2R = 302 -----------------> Rearrange to gather like terms

336-302 = R -----------------> Move the R's to left and numbers to right side of Eq.

R = 34 -----------------> Hey! We've determined that R is 34!!!!

Now we go back to Eq 1 and replace R with 34:

1) C = 112-34

C = 88

That's it: 88 Carnation Corsages

34 Rose Corsages

The key to solving this, Marina, is that we defined two variables (C and R) and then wrote two equations expressing the given information. The result was two variables and two equations. Then we solved them in two steps.

Let me know if this helped, OK?

John S.