SOLUTION: Your maximum exercise heart rate M is given by the formula M = 0.85(220-a), where "a" is your age. What is the age of someone who has a maximum exercise heart rate of 133?

Question 87216: Your maximum exercise heart rate M is given by the formula M = 0.85(220-a),
where "a" is your age. What is the age of someone who has a maximum exercise heart rate of 133?
Found 2 solutions by checkley75, bucky:
Answer by checkley75(3666) (Show Source): You can put this solution on YOUR website!
M=.85(220-A)
133=.85(220-A)
133=187-.85A
.85A=187-133
.85A=54
A=54/.85
A=63.5
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
Given:
.
M = 0.85(220 - a)
.
and also given that M = 133
.
Find "a"
.
Method:
.
Substitute 133 for M in the equation to get:
.
133 = 0.85(220 - a)
.
Multiply 0.85 times each of the quantities in the parentheses:
.
133 = 0.85*220 - 0.85*a
.
Note that 0.85 times 220 is 187. When you do that multiplication, the equation becomes:
.
133 = 187 - 0.85a
.
Next you need to get the term containing "a" by itself on one side of the equation, and
everything else on the other side. Let's begin by adding 0.85a to BOTH sides of the equation.
When you do, the addition of 0.85a to the right side cancels the -0.85a on the right side.
This makes the equation become:
.
133 + 0.85a = 187
.
Subtract 133 from both sides to get rid of it on the left side. When you subtract
133 the equation becomes:
.
0.85a = 187 - 133
.
The subtraction on the right side results in:
.
0.85a = 54
.
Divide both sides by the multiplier of "a" to solve for "a". When you do that the equation
becomes:
.
a = 54/0.85
.
and the right side is:
.
a = 63.5294
.
which tells you that at the age of 63.5 years the maximum rate of heart exercise is 133.
.
You can check this by substituting 63.5 into the original equation to find that:
.
M = 0.85(220 - 63.5)
.
Subtract the two numbers in parentheses to get:
.
M = 0.85(156.5)
.
do the multiplication and the result is:
.
M = 133.025
.
The slight difference is due to rounding off the number of years. So the answer we got in
this checking work is equal to the heart rate specified by the problem ... 133.
.
Hope this helps you to understand how to work the problem.

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