# Math Lesson 8.1.5 - Substituting in Formulas derived from Wordy Problems

Welcome to our Math lesson on Substituting in Formulas derived from Wordy Problems, this is the fifth lesson of our suite of math lessons covering the topic of Writing Formulas and Substituting in a Formula, you can find links to the other lessons within this tutorial and access additional Math learning resources below this lesson.

## Substituting in Formulas derived from Wordy Problems

Wordy problems contain the necessary information to produce one or more formula; you just have to identify the variables participating in the event. This is similar to the mining process used to extract minerals from the Earth core. Then, you can write the equations and apply the same procedure as the one explained earlier.

### Example 6

The ratio of Laura's trophies to Anne's trophies is 7:4. The difference between the numbers is 12. What are the numbers?

### Solution 6

This is a problem involving ratios, for which we have discussed in chapter 4. We can use a common factor k to reduce the number of variables in the formula. Thus, instead of writing

L:A = 7:4

where L is for Laura and A for Anne, we write instead

L/7 = A/4 = k

so,

L = 7k and A = 4k

L - A = 12

Therefore, the formula used in this problem is

7k - 4k = 12

It helps calculate the common factor k, i.e.

3k = 12
k = 4

Now, we can find the number of trophies won by each girl. Thus, for Laura, we have

L = 7k = 7 ∙ 4 = 28

and for Anne, we have

A = 4k = 4 ∙ 4 = 16

Let's consider another wordy problem including banking.

### Example 7

A customer deposits \$15,000 in a bank that applies compound interest rates. If the interest rate is 0.8% and it is compound twice a year, calculate the total amount the customer will have in his savings account after four years.

### Solution 7

We have explained the compound interest formula

An (t) = P ∙ (1 + r/n)n ∙ t

in tutorial 5.4, where

An (t) → the amount of deposit after t years;

P → principal (original deposit);

r → interest rate expressed as a decimal (here r = 0.8% = 0.8/100 = 0.008);

n → number of compounds in a year; and

t → time of deposit (in years)

In our example, we have the following values:

P = 15,000
r = 0.008
n = 2
t = 4

In this way, we obtain for the amount the customer will have in his savings account after four years:

An (4) = 15,000 ∙ (1 + 0.008/2)2∙4
= 15,000 ∙ (1 + 0.004)8
= 15,000 ∙ 1.0048
= 15,000 ∙ 1.03245
= 15,486.75

Thus, the customer will have \$15,486.75 in his savings account after four years of deposit.

## More Writing Formulas and Substituting in a Formula Lessons and Learning Resources

Formulas Learning Material
Tutorial IDMath Tutorial TitleTutorialVideo
Tutorial
Revision
Notes
Revision
Questions
8.1Writing Formulas and Substituting in a Formula
Lesson IDMath Lesson TitleLessonVideo
Lesson
8.1.1Mathematical vs Word Sentences
8.1.2What is a Formula? How do we Write Formulas?
8.1.3Expressing Events in a Shorter Way using Formulas
8.1.4Substituting into a Formula
8.1.5Substituting in Formulas derived from Wordy Problems
8.1.6Finding the Inverse Formula

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