Chapter 2: Q. 71 (page 113)

In the following exercises, solve each equation with decimal coefficients.
$0.10 d + 0.25 (d + 5) = 4.05$

Short Answer

Expert verified

The value of $d$ is $8$

Step by step solution

Step 1. Given Information

In the given question we have to solve equation with decimal coefficients.
$0.10 d + 0.25 (d + 5) = 4.05$

Step 2. The given equation is 0.10d+0.25(d+5)=4.05

Now we solve the given equation for the value of $d$

Looking at the decimals and thinking of the equivalent fractions:

$0.10 = \frac{10}{100} 0.25 = \frac{25}{100} 4.05 = \frac{405}{100}$

The LCD is 100.

Step 4. By multiplying by the LCD we will clear the decimals from the equation.

Distribute first.

$0.10 d + 0.25 \times d + 0.25 \times 5 = 4.05 0.10 d + 0.25 d + 1.25 = 4.05$

Combine like terms.

$0.35 d + 1.25 = 4.05$

Step 5. To clear decimals, multiply by 100.

$100 (0.35 d + 1.25) = 4.05 \times 100$

Distribute.

$100 \times 0.35 d + 100 \times 1.25 = 4.05 \times 100 35 d + 125 = 405$

Step 6. Subtract 125 on both side

$35 d + 125 - 125 = 405 - 125 35 d = 280 \frac{35}{35} d = \frac{280}{35} d = 8$

Step 7. Now checking the value.

putting $d = 8$ in the given equation

$0.10 \times 8 + 0.25 (8 + 5) = 4.05 0.80 + 0.25 (13) = 4.05 0.80 + 3.25 = 4.05 4.05 = 4.05$

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In the following exercises, solve each equation with decimal coefficients.
$0.10 d + 0.25 (d + 5) = 4.05$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. The given equation is 0.10d+0.25(d+5)=4.05

Looking at the decimals and thinking of the equivalent fractions:

Step 4. By multiplying by the LCD we will clear the decimals from the equation.

Step 5. To clear decimals, multiply by 100.

Step 6. Subtract 125 on both side

Step 7. Now checking the value.

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In the following exercises, solve each equation with decimal coefficients.0.10d+0.25(d+5)=4.05

Short Answer

Step by step solution

Step 1. Given Information

Step 2. The given equation is 0.10d+0.25(d+5)=4.05

Looking at the decimals and thinking of the equivalent fractions:

Step 4. By multiplying by the LCD we will clear the decimals from the equation.

Step 5. To clear decimals, multiply by 100.

Step 6. Subtract 125 on both side

Step 7. Now checking the value.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Applied Mathematics

Probability and Statistics

Pure Maths

Geometry

Mechanics Maths

Study anywhere. Anytime. Across all devices.

In the following exercises, solve each equation with decimal coefficients.
$0.10 d + 0.25 (d + 5) = 4.05$