Transcript Decimal Equations

OBJECTIVE
• I will use the order of operations and
rounding to find the exact and
approximate solutions of equations that
contain decimals.
Rounding for a Practical Answer
Six people buy some food to take to the lake. The
total cost for the food is $33.45. If each person
pays the same amount, how much does each
person owe?
6x = 33.45 Original equation
x = 5.575
Exact answer
x ≈ 5.58
Round to the nearest cent
Each person owes $5.58. The exact answer is not
practical because you cannot have a fraction of a
cent, but six times the rounded answer does not
correspond to the cost of the food. It is one cent
too much due to round-off error.
Rounding for the Final Answer
Solve 7x + 32 = 128. Round to the nearest
hundredth.
7x + 32 = 128
Original equation
7x = 96
Subtract 32 from each side
x = 13.714…
Divide both sides by 7
x ≈ 13.71
Round to nearest hundredth
The solution is approximately 13.71.
Guided Practice
1. Solve -12x - 13 = 37. Round to the
nearest hundredth.
Original Equation Involving
Decimals
• Solve using same methods used to solve
equations without a decimal.
Solve 2.14x + 3.81 = 0.53x + 14.96. Round to
the nearest hundredth.
2.14x + 3.81 = 0.53x + 14.96
1.61x = 11.15
x = 6.925…
x ≈ 6.93
Guided Practice
1. Solve 7.82x - 3.14 = 4.66x + 2.71.
Round your answer to the nearest
hundredth.
Changing Decimal
Coefficients to Integers
• Change decimals to integers for easier calculation
Solve 2.3x + 6.2 = 1.5x + 9.8. Round to the nearest
tenth.
2.3x + 6.2 = 1.5x + 9.7
Original Equation
23x + 62 = 15x + 97
Multiply both sides by 10
8x = 35
Combine like terms
x = 4.625
x ≈ 4.6
Guided Practice
Re-write the coefficients as integers and
solve. Round to the nearest tenth.
1. 5.7 - 3.4x = 2.2x - 7.1
Using a Verbal Model
You are shopping for roses. The total tax
is 10%. You have a total of $27.79 to
spend. What is your price limit for the
roses?
Total cost is price limit and tax based on
price limit.
Using a Verbal Model
Cost of Roses + Cost of Tax = Price Limit
x + 0.10x = 27.79 Substitute
1.10x = 27.79
Combine like terms
x = 25.263…
Divide both sides by 1.10
x ≈ 25.26
Round down
You have a limited amount of money to
spend, so you must round down to $25.26. If
you round up, the tax and total cost will
increase and you will be a penny short.
Guided Practice
You are shopping for a bracelet. The
sales tax is 5%. You have a total of
$125.40 to spend. What is your price
limit for the bracelet?
Independent Practice
Round answers to the nearest hundredth.
1. 3x + 5 = 20
2. 2.51x - 4.27 = 1.13x + 2.15
3. Change the decimal coefficients to
integers to solve.
3.4x - 2.3 = 1.7x + 5.4