JohnB
01-15-2008, 08:52 PM
A student has asked me to explain problem 8 in MR's Math Study Guide. Here's the problem:
The relationship between m and n is described by: 11m = 5(n - 42). If the difference between two chosen values of n is 30, what is the difference in the corresponding values of m?
A) 30/11 B) 42/11 C) 60/11 D) 150/11 E) 14
We can approach this in a couple of ways. There's the algebraic approach. Let's begin by getting m by itself on the left side (since we're looking for values of m):
11m = 5n - 210
m = (5/11)n - 210/11
Let's call n1 the smaller value of n, and m1 the smaller value of m. The larger values will be n2 and m2. Then:
m1 = (5/11)n1 - 210/11
m2 = (5/11)n2 - 210/11.
But we also know that
n2 = n1 + 30. So:
m2 = (5/11)(n1 + 30) - 210/11
= (5/11)n1 + 150/11 - 210/11
= [(5/11)n1 - 210/11] +150/11
= m1 + 150/11.
So our answer is 150/11.
We can also try plugging in numbers for our variables. Let's choose numbers that will make the equations easy to work with. Since our equation uses the expression (n - 42), I'll choose 42 for my smaller n and 72 for my larger (remember, they differ by 30). I'll still use m1 for the smaller value of m and m2 for the larger.
11m1 = 5(42 - 42) = 5(0) = 0
m1 = 0.
11m2 = 5(72 - 42) = 5(30) = 150
m2 = 150/11.
So again, the difference is 150/11.
The relationship between m and n is described by: 11m = 5(n - 42). If the difference between two chosen values of n is 30, what is the difference in the corresponding values of m?
A) 30/11 B) 42/11 C) 60/11 D) 150/11 E) 14
We can approach this in a couple of ways. There's the algebraic approach. Let's begin by getting m by itself on the left side (since we're looking for values of m):
11m = 5n - 210
m = (5/11)n - 210/11
Let's call n1 the smaller value of n, and m1 the smaller value of m. The larger values will be n2 and m2. Then:
m1 = (5/11)n1 - 210/11
m2 = (5/11)n2 - 210/11.
But we also know that
n2 = n1 + 30. So:
m2 = (5/11)(n1 + 30) - 210/11
= (5/11)n1 + 150/11 - 210/11
= [(5/11)n1 - 210/11] +150/11
= m1 + 150/11.
So our answer is 150/11.
We can also try plugging in numbers for our variables. Let's choose numbers that will make the equations easy to work with. Since our equation uses the expression (n - 42), I'll choose 42 for my smaller n and 72 for my larger (remember, they differ by 30). I'll still use m1 for the smaller value of m and m2 for the larger.
11m1 = 5(42 - 42) = 5(0) = 0
m1 = 0.
11m2 = 5(72 - 42) = 5(30) = 150
m2 = 150/11.
So again, the difference is 150/11.