I need help solving these three problems.

1/4(7 + 3g) + -g/8

Twice the greater of two consecutive odd integers is 13 less than three times the lesser number. Find the integers.

About 4.9 million households had one brand of personal computers in 2001. The use of these computers grew at an average rate of 0.275 million households a year. In 2001, about 2.5 million households used another type of computer. The use of these computers gew at an average rate of 0.7 million households a year. How long will it take for the two types of computers to be in the same number of households?

Thanks.

For the first one, are you simplifying?

1/4(7 + 3g) + -g/8
= (7+3g)/4 - g/8
= (14 + 6g)/8 - g/8
= (14 + 5g)/8

For the second, solve
2(x+2) = 3x - 17

For the third, let t=0 correspond with the year 2001
so C1 = .275t + 4.9
and C2 = .7t + 2.5

Now equate C1 and C2
.275t+4.9 = .7t+2.5
275t + 4900 = 700t + 2500
2400 = 425t
t = 5.6 yrs.

Sure, I can help you with those problems. Let's start with the first one:

1/4(7 + 3g) + -g/8

To solve this problem, we need to simplify the expression.

Step 1: Distribute the 1/4 to the terms inside the parentheses:
(1/4) * 7 + (1/4) * (3g) + -g/8

Step 2: Simplify each term:
7/4 + (3/4)g + -g/8

Step 3: Find a common denominator for the fractions: 8
(7/4)*(2/2) + (3/4)g + -(g/8)*(1/1)

Step 4: Simplify the fractions with the common denominator:
14/8 + (3/4)g + -g/8

Step 5: Combine like terms:
(14/8 - g/8) + (3/4)g
(14 - g)/8 + (3/4)g

So, the simplified form of the expression is (14 - g)/8 + (3/4)g.

Now, let's move on to the second problem:

Twice the greater of two consecutive odd integers is 13 less than three times the lesser number. Find the integers.

Let's assume the first odd integer is x. The second consecutive odd integer would be x +2.

According to the problem, the equation would be:

2(x+2) = 3x - 13

Step 1: Distribute 2 on the left side:
2x + 4 = 3x - 13

Step 2: Move terms with x to one side and constant terms to the other side:
2x - 3x = - 13 - 4
-x = -17

Step 3: Divide by -1 to solve for x:
x = 17

Step 4: Substitute the value of x back into the equation to find the second integer:
x + 2 = 17 + 2 = 19

Therefore, the two consecutive odd integers are 17 and 19.

Finally, let's move on to the third problem:

We are given two growth rates for two different types of computers. We need to find the number of years it will take for the two types of computers to have the same number of households.

Let's assume the number of years is represented by y.

The growth rate for the first brand of computers is 0.275 million households per year. So, the number of households for the first brand after y years would be:

4.9 + 0.275y

The growth rate for the second brand of computers is 0.7 million households per year. So, the number of households for the second brand after y years would be:

2.5 + 0.7y

To find the number of years it will take for the two types of computers to be in the same number of households, we need to set the two expressions equal to each other and solve for y:

4.9 + 0.275y = 2.5 + 0.7y

Step 1: Move terms with y to one side and constant terms to the other side:
0.275y - 0.7y = 2.5 - 4.9
-0.425y = -2.4

Step 2: Divide by -0.425 to solve for y:
y = -2.4 / -0.425

Step 3: Simplify the value of y:
y ≈ 5.647

Therefore, it will take approximately 5.647 years for the two types of computers to have the same number of households.

I hope this helps! Let me know if you have any further questions.