Ashley
question level: 10-12
Student

Hi, I have questions about solving the two math problems below. I've looked at them both for about two hours. I just completely don't understand them. Thanks so much for taking time to help me, I greatly appreciate it.

Question 1: For all values of a, let < a > be defined as < a > = 4a - 4 . Which of the following equals < 6 > - < 5 >?

A: < 2 >
B: < 3 >
C: < 4 >
D: < 5 >
E: < 6 >

Question 2: If 5n + p = 3 and 2m - 10n = 2, what is the value of m + p?

Thanks again,
Ashley



Hi Ashey,

The notation < a > = 4a - 4 is means that whenever you see a number surrounded by the angle brackets you should replace it with 4 times the number minus 4. So, for example

< 3 > = 4x3 - 4 = 12 - 4 = 8 and < 7 > = 4x7 - 4 = 28 - 4 = 24 Hence for question 1 find < 6 > and < 5 > and then subtract < 5 > from < 6 >

For question 2, p appears in the first equation and m appears in the second. Thus use the first equation to find P and the second equation to find m. Finally add p and m.

Finding p:
5n + p = 3 and the goal is to manipulate the equation to end with an equation of the form p = ???

p can be isolated to the left of the equal sign by subtracting 5n from both sides. Thus

5n + p - 5n = 3 - 5n In other words p = 3 - 5n

Finding m:
The second equation is 2m - 10n = 2. This time you can add 10n to both sides to get

2m - 10n + 10n = 2 + 10n or 2m = 2 + 10n To isolate m all that remains is to divide both sides by 2. That is m = (2 + 10n)/2 = 2(1 + 5n)/2 = 1 + 5n Finally add p and m.

I hope this helps,
Penny
Go to Math Central