Roses cost $3 and tulips cost $2. Eva can spend at most $40. Write… Step by Step

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The question

Question: Roses cost $3 and tulips cost $2.

Eva can spend at most $40.

Write the inequality.

1 Find what we know

What do we know?

Roses cost $3 each.

Tulips cost $2 each.

Eva can spend $40 or less.

What do we want?

An inequality for this story.

2 Name the unknowns

We don't know how many roses.

We call that number x.

x = number of roses

We don't know how many tulips either.

It is a different number, so it gets its own letter: y.

y = number of tulips

3 Write the inequality

One rose costs $3.

So x roses cost 3 times x: 3x.

x roses: 3 × x = 3x

One tulip costs $2.

So y tulips cost 2 times y: 2y.

y tulips: 2 × y = 2y

At most $40 means $40 or less.

That is the sign less than or equal to.

at most $40 = $40 or less: ≤

In words: the rose money plus the tulip money is at most $40.

3x + 2y = 40

So the inequality is 3x + 2y ≤ 40.

3x + 2y ≤ 40

Careful!

At most means 40 or less.

So the sign is less than or equal to, not more than.

Careful: not 3x + 2y ≥ 40 ✗

4 Check

Let's test it with two buys: a small one and a big one.

1 rose and 1 tulip cost $5.

That is at most $40, and the inequality says true.

x = 1, y = 1: 3 + 2 = 5 ≤ 40 true

14 roses cost $42.

That is more than $40, and the inequality says false.

Both match the story.

It works!

x = 14, y = 0: 3 × 14 = 42 not ≤ 40 false

Let's look back.

First: find what we know.

Then: name the unknowns.

Then: write the inequality.

Last: check.

Answer