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Translate to a system of equations and then solve:

Mark went to the gym and did 40 minutes of Bikram hot yoga and 10 minutes of jumping jacks. He burned 510 calories. The next time he went to the gym, he did 30 minutes of Bikram hot yoga and 20 minutes of jumping jacks burning 470 calories. How many calories were burned for each minute of yoga? How many calories were burned for each minute of jumping jacks?

Mark burned 11 calories for each minute of yoga and 7 calories for each minute of jumping jacks.

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Translate to a system of equations and then solve:

Erin spent 30 minutes on the rowing machine and 20 minutes lifting weights at the gym and burned 430 calories. During her next visit to the gym she spent 50 minutes on the rowing machine and 10 minutes lifting weights and burned 600 calories. How many calories did she burn for each minutes on the rowing machine? How many calories did she burn for each minute of weight lifting?

Erin burned 11 calories for each minute on the rowing machine and 5 calories for each minute of weight lifting.

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Solve geometry applications

When we learned about Math Models , we solved geometry applications using properties of triangles and rectangles. Now we’ll add to our list some properties of angles.

The measures of two complementary angles    add to 90 degrees. The measures of two supplementary angles    add to 180 degrees.

Complementary and supplementary angles

Two angles are complementary if the sum of the measures of their angles is 90 degrees.

Two angles are supplementary if the sum of the measures of their angles is 180 degrees.

If two angles are complementary, we say that one angle is the complement of the other.

If two angles are supplementary, we say that one angle is the supplement of the other.

Translate to a system of equations and then solve:

The difference of two complementary angles is 26 degrees. Find the measures of the angles.

Solution

Step 1. Read the problem. Step 2. Identify what we are looking for. We are looking for the measure of each angle. Step 3. Name what we are looking for. Let x = the measure of the first angle. y = the measure of the second angle Step 4. Translate into a system of equations. The angles are complementary. x + y = 90 The difference of the two angles is 26 degrees. x y = 26 The system is { x + y = 90 x y = 26 Step 5. Solve the system of equations by elimination. { x + y = 90 x y = 26 _________ 2 x = 116 x = 58 Substitute x = 58 into the first equation. x + y = 90 58 + y = 90 y = 32 Step 6. Check the answer in the problem. 58 + 42 = 90 58 32 = 26 Step 7. Answer the question. The angle measures are 58 degrees and 42 degrees.

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Translate to a system of equations and then solve:

The difference of two complementary angles is 20 degrees. Find the measures of the angles.

The angle measures are 55 degrees and 35 degrees.

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Translate to a system of equations and then solve:

The difference of two complementary angles is 80 degrees. Find the measures of the angles.

The angle measures are 5 degrees and 85 degrees.

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Translate to a system of equations and then solve:

Two angles are supplementary. The measure of the larger angle is twelve degrees less than five times the measure of the smaller angle. Find the measures of both angles.

Solution

Step 1. Read the problem.
Step 2. Identify what we are looking for. We are looking for the measure of each angle.
Step 3. Name what we are looking for. Let x = the measure of the first angle.
y = the measure of the second angle
Step 4. Translate into a system of equations. The angles are supplementary.
.
The larger angle is twelve less than five times the smaller angle
.
The system is:


Step 5. Solve the system of equations substitution.
.
Substitute 5 x − 12 for y in the first equation. .
Solve for x . .
.
.
Substitute 32 for in the second equation, then solve for y . .
.
.
Step 6. Check the answer in the problem.

32 + 158 = 180 5 · 32 12 = 147
Step 7. Answer the question. The angle measures are 148 and 32.
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Practice Key Terms 2

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Source:  OpenStax, Elementary algebra. OpenStax CNX. Jan 18, 2017 Download for free at http://cnx.org/content/col12116/1.2
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