Algebra Honors (Periods 6 & 7)

 Using Equations to Solve Problems 3-4

We looked at several problems in our textbook on Page 113-114
8. Find three consecutive ODD integers whose sum is 105
Let x = the first odd integer
let x + 2 = 2nd odd integer
Let x +4 = the 3rd odd integer

x + (x +2) + (x + 4) = 105
3x + 6 = 105
3x = 99

x = 33
{33, 35, 37}

10. Five consecutive integers whose sum is 195

let x = the 1st integer
x + 1 = the 2nd
x + 2 = 3rd
x + 3 = 4th
x + 4 = 5th
x + (x +1) + (x + 2) + (x + 3) + (x + 4)  =195
5x + 10 = 195
5x = 185
x = 37
{37, 38, 39, 40, 41}

12.  New tank holds 350 barrels of oil more than the old tank. Together they hold 3650 barrels of oil. How much does each hold?

Let x = the # of barrels in the old tank
let x + 350 = the # of barrels in the new tank
x + (x +350) = 3650

2x = 3300
x = 1650
The old tank holds 1650 barrels of oil
The new tank holds 2000 barrels of oil


23.  Angle A is 3 times as large as Angle B and Angle A is 16 degrees larger than Angle C

If you let x = the measure f Angel A
then
x/3 = measure of Angle B
x-16 = measure of Angle C
This became a bit complicated for some
But..
 x + (1/3)(x) + x - 16 = 180
(7/3)x - 16 = 180
(7/3)x = 196
x = 84
So Angle A is 84 degrees
Angle B is 24 Degrees
Angle C is  68 Degrees

But you could have set your variables as
Let x = the measure of Ange b
Then
3x = the measure of Angle A
3x -16 = the measure of Angle C
x + 3x + (3x - 16) = 180
x = 28
and you still get the same solutions
So Angle A is 84 degrees
Angle B is 24 Degrees
Angle C is  68 Degrees