# Math in the Super Market

Shopping often involves discount and sale price. But having a good number sense will make you a better consumer. In this article we will examine and compare common sales offers used in retail stores.

When we go shopping, mathematics plays a crucial role in several aspects of our experience, from budgeting and calculating discounts to understanding unit prices and making informed decisions about purchases. Let’s delve into the ways math intertwines with the shopping process.

Before heading to the store or making an online purchase, we often create a budget to manage our expenses effectively. This involves mathematics as we calculate our total income, subtract fixed expenses such as rent or mortgage payments, utilities, and savings, and then allocate the remaining funds for shopping. This basic arithmetic helps us ensure that we don’t overspend and stay within our financial means.

Once we’re at the store, we encounter various mathematical concepts. One of the most common calculations is determining the total cost of items we intend to purchase. We multiply the price of each item by the quantity we want to buy and then sum up these individual costs to find the overall total. This fundamental arithmetic skill helps us keep track of our spending and ensures we don’t exceed our budget.

Discounts and promotions are prevalent in retail environments. Understanding how these discounts affect prices requires mathematical reasoning. For example, when a store offers a discount of 20% off the original price of an item, we use percentages to calculate the discounted price. It involves finding 20% of the original price and subtracting that amount from the original price. This calculation allows us to determine the final price we’ll pay after the discount is applied.

Unit pricing is another important mathematical concept in shopping. It involves comparing the prices of similar items based on their quantity or weight. By examining the unit price, which is usually displayed on the price tag, we can determine which product offers the best value for money. For instance, if we’re comparing two brands of cereal, one priced at \$3.50 for 400 grams and the other at \$4.00 for 500 grams, we can use division to find the cost per gram and determine which option is more economical.

Suppose you’re in the cereal aisle and trying to decide between two different brands of oatmeal. Brand A offers a 500g package for \$4.50, while Brand B offers a 750g package for \$6.00.

To compare the unit prices of these two options, you’ll need to calculate the cost per gram for each brand.

For Brand A: Package size: 500g, Price: \$4.50

To find the cost per gram, divide the total price by the package size:

Cost per gram for Brand A = \$4.50 / 500 grams

Cost per gram for Brand A=\$0.009 per gram

For Brand B: Package size: 750g, Price: \$6.00

Similarly, to find the cost per gram for Brand B:

Cost per gram for Brand B = \$6.00 / 750 grams

Cost per gram for Brand B = \$0.008 per gram

Now that you have the cost per gram for each brand, you can see that Brand B offers a lower cost per gram compared to Brand A.

Even though Brand B has a higher upfront price (\$6.00 compared to \$4.50 for Brand A), when you calculate the cost per gram, you’ll find that Brand B is more economical at \$0.008 per gram compared to Brand A’s \$0.009 per gram.

When making larger purchases, such as furniture or electronics, we often encounter complex pricing structures, including sales tax, delivery fees, and optional warranties. Calculating the total cost requires adding these additional expenses to the base price of the item. Sales tax, for instance, is typically expressed as a percentage of the purchase price, and we use multiplication to calculate the tax amount. Including these extra costs in our calculations ensures that we have an accurate understanding of the total expenditure involved.

In addition to basic arithmetic, mathematics also plays a role in evaluating deals and comparing prices across different stores or online platforms. This involves analyzing percentages, ratios, and equations to determine which option offers the best value. By conducting these mathematical assessments, we can make informed decisions and maximize our purchasing power.

Mathematics permeates every aspect of the shopping experience, from budgeting and calculating discounts to comparing prices and evaluatig deals. By leveraging mathematical principles, we can manage our finances effectively, make informed purchasing decisions, and ensure that we get the most value for our money.

### Specific Examples

Buy 1, Get 1 Free. In this world, nothing is free. The best way to compute the cost per item is to take the price for one item, and divide by two. Then you can determine if this is a good price. For example, if the price for one is \$19.99, then the cost per item is roughly \$20 divided by 2, or \$10 each.

Buy 2, Get the Third free. The best way to compute the cost per item is to take the price for two items, and divide by three. Then you can decide if this is a good price. For example, if the price for one is \$7.49, then the cost per item is roughly \$15 divided by 3, or \$5 each.

Buy 1, Get One 1/2 Price. If the price for one is \$19.99, then the cost per item is approximately the sum of \$20 and \$10, divided by 2, which is \$15.

Buy 1, Get the Second for \$1. If the price for one is \$19.99, then the cost per item is about \$21 divided by 2, or \$10.50.

For each of the offers above, we computed the actual cost per item. Once you know the actual cost, you can determine if an offer is a good, and the true value it presents.

Another common technique for boosting retail sales is through coupon offers. If there is more than one coupon, things can get confusing. For our first example, suppose the same store offers you these coupons:

1. 20% off any purchase
2. \$10 off your purchase of \$30 or more

Which coupon would you choose and why? The answer depends on how much you buy from the store. The first coupon is a discount rate of 20% — the discount will vary in direct proportion to the amount of your purchase. The second coupon is a fixed amount off a minimum buy. Let’s compare these coupons for several purchase amounts to see which one saves you more.

 Ex. 1 How Much Will You Save? purchase 20% off \$10 off \$30 or more \$20 \$4 \$0 \$25 \$5 \$0 \$30 \$6 \$10 \$35 \$7 \$10 \$40 \$8 \$10 \$45 \$9 \$10 \$50 \$10 \$10 \$55 \$11 \$10 \$60 \$12 \$10

In example 1, the break-even point is a purchase of \$50. For our second example, suppose the same store offers you these coupons:

1. \$25 off your purchase of \$100 or more

Once again, which coupon you choose depends on how much you buy. Let’s compare these coupons for several purchase amounts to see which one saves you more.

 Ex. 2 How Much Money Will You Save? purchase 20% off \$25 off \$100 or more \$25 \$5 \$0 \$50 \$10 \$0 \$75 \$15 \$0 \$100 \$20 \$25 \$125 \$25 \$25 \$150 \$30 \$25 \$175 \$35 \$25 \$200 \$40 \$25

In example 2, the break-even point is a purchase of \$125.

In the problems above, we computed the amount saved for each coupon (i.e., the discount). To compute the sale price (the amount you actually pay), you would have to subtract the discount from your purchase amount. If you only have a certain amount of money to spend, then sometimes it is easier to compute the sale price directly. To do this, take the discount rate and subtract it from 100%, then multiply the result by your purchase amount. In the case of 20% off, you would multiply your purchase amount by 80% to get the amount you will actually pay. This is shown in example 3 below.

 Ex. 3 How Much Money Will You Pay? purchase 20% off \$10 off \$30 or more \$20 \$16 \$20 \$25 \$20 \$25 \$30 \$24 \$20 \$35 \$28 \$25 \$40 \$32 \$30 \$45 \$36 \$35 \$50 \$40 \$40 \$55 \$44 \$45 \$60 \$48 \$50

In example 3, the break-even point is a purchase of \$50.

The information above might be common sense for some readers, and an eye-opener for others. From my experience, people vary widely when it comes to number sense and shopping habits. In any event, it is good to be able to catch a cashier’s errors when making a purchase.