Using Equations to Solve Business Problems

Today managers must have the ability to analyze the facts of a business problem and devise custom-made formulas to solve them.

coefficient A number or quantity placed before another quantity, indicating multiplication.

For example, 4 is the coefficient in the expression 4C. This indicates 4 multiplied by C.

transpose To move a term from one side of an equation to the other. Whenever addition or subtraction is used for moving the term, a corresponding change of sign occurs.

When a written statement has no action word (verb), it is an expression. When there is a verb such as is, it represents an equal sign and the statement is an equation.

For the following statements, underline the key words and translate into expressions.1. A number increased by 18 2. 19 times W3. 12 less than S 4. 2/3 of Y5. 9 more than 2 times R 6. 4 times the quantity of X and 87. The sum of twice E and 98. 6 times N divided by Z9. 8 less than half of F10. ₱45.75 more than the product of X and Y11. The difference of Q and 4412. R times A times B

For the following statements, underline the key words and translate into expressions.13. A number decreased by 14 is 23.14. 8 less than 3D leaves 19.15. A number totals 4 times the quantity of V and N.16. The cost of X lb at $3 per lb is $12.17. Cost is the product of price and quantity.18. The sum of liabilities and capital is assets.19. What number increased by 32 yields 125?20. 21 less than twice C gives 9.21. 5 more than 6 times a number plus 3 times that number is 25.22. The cost of G gallons at $1.33 per gallon equals $34.40.23. The area of a rectangle is the length times the width.24. (Challenge) What number less 12 is the average of A, B, and C?

Grouping symbols are used to arrange numbers, variables, and operations. In this chapter, you learned to use the grouping symbols known as:parentheses ( ) , brackets [ ] and braces { }.

When solving equations with multiple grouping symbols, always start with the innermost symbols and work to the outside.

X = 6(2 + [3{9 – 3} + {8 + 1} – 4])

1. On Tuesday, Double Bubble Car Wash took in ₱3600 less in wash business than in wax business. If the total sales for the day were ₱9200, what were the sales for each service?

2. Don and Chuck are salespeople for Security One Alarms. Last week Don sold 12 fewer alarm systems than Chuck did. Together they sold 44. How many did each sell?

3. Dynamic Industries Inc., spends 1/4 of total revenue on employee payroll expenses. If last week’s payroll amounted to ₱50,000, what was the revenue for the week?

4. One-third of the checking accounts at the Community Bank earn interest. If 2,500 accounts are this type, how many total checking accounts does the bank have?

5. United Dynamics, Inc., has 25 shareholders. If management decides to split the ₱80,000 net profit equally among the shareholders, how much will each receive?