1. You want to plant a flower garden in your yard so that you can make a beautiful bouquet to put on the alter at church for Easter Sunday services. There are two types of flowers that you are going to be planting. You will be planting some tulips and daffodils. At the store tulips come in packs of 6 and daffodils come in packs of 9.

a.What is the least amount of packs of daffodils and tulips you would need to buy to have the same amount of each?

b.How many should you have of each kind of flower?

2.Each pack of tulips costs $4.75 and each pack of daffodils cost $3.50. From the previous problem, you know how many packs of each you will need. The sales tax is 7.5%.
a.How much tax will you be paying for all the flowers, to the nearest cent?

b.How much total will you be paying for all flowers, to the nearest cent?

3.You remember that you have a discount coupon for $2.75 off your total purchase before tax.
a. How much did the flowers cost with the discount including tax (Round to the nearest penny)?

b.How much money did you save with the coupon including tax?

You want the least number of flowers and the number of packs you must purchase to have the same number of tulips and daffodils when tulips come in a 6-pack for $4.75 and daffodils come in a 9-pack for $3.50. You also want the amount of tax at 7.5%, the with-tax cost after a $2.75 discount coupon, and the total savings (with tax) that the coupon gives.

1b. Flowers

The least common multiple of 6 and 9 is (6·9)/3 = 18. This is the number of flowers of each kind you will have.

You will have 18 of each kind of flower.

1a. Packs

At 6 per pack, you will need 18/6 = 3 packs of tulips.

At 9 per pack, you will need 18/9 = 2 packs of daffodils.

You need to buy 3 packs of tulips and 2 packs of daffodils.

2a. Tax

The tax on the purchase will be the product of the tax rate and the total amount of the purchase. That total amount is sum of the product of the number of packs and the cost per pack for each of the types of flowers.

tax = 7.5% × (3×$4.75 +2×$3.50) = $1.59

2b. Total

The total cost of the flowers is ...

(3×$4.75 +2×$3.50) × (1 +0.075) = $22.84

3a. Discounted

When a discount coupon is applied, the total cost is ...

(3×$4.75 +2×$3.50 - $2.75) × (1 +0.075) = $19.89

3b. Savings

The savings with the coupon is ...

$22.84 -19.89 = $2.95

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Additional comment

You can figure the individual costs and add them up, or you can simply tell the calculator to do all that. We have elected to write the computations using a minimum number of calculator entries. In some cases, intermediate results are required for answering parts of the question.

In the least common multiple (LCM) calculation above, we have computed it as the product of the numbers, divided by their greatest common factor (3).

The "dot product" of lists {a, b} and {c, d} is ac +bd. It actually takes more keystrokes to write the sum of products using the DotP function.

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