Answer:
1. 6w+6=48
2. n = 9
3. 2x+2 = 5.64
4. 2x-3 = 7.80
5. 2x+6 = 30
6. 3x+3 = 153
7. 2x - 6 = 14
8. 3x + 6 = 54
9. 1424 = 356*t
Explanation:
1.
Let the width be w, then twice the width is 2w. But our length is 3 more than twice the width, implying that our length will be 2w+3.
The perimeter of a rectangle is given by the formula;
p = 2(length + width)
2(2w+3+w) = 48
6w+6=48 is our required equation.
2.
Fifteen more than four times a number is 6 more than five times the number. Use "n" for the number.
We first evaluate, Fifteen more than four times a number;
since our number is n, the above statement can be written mathematically as,
4n + 15
The next step we evaluate; five times the number,
5n
In the final step we compare these two expression and solve for n;
we have been told that; Fifteen more than four times a number is 6 more than five times the number. This implies;
4n + 15 - 5n = 6
-n = -9
n = 9
3.
Let the amount paid by Martha be x. Therefore, the amount paid by Sally would be x+2 since she paid 2 more than Martha. The total amount paid by both is;
x+x+2 = 2x+2
The required equation is thus;
2x+2 = 5.64
4.
We let the amount spent by Tim be x. This would mean that Bob spent x-3 since we are told that Bob paid $3 less than Tim. Therefore, the total amount spent by Bob and Tim in terms of x is;
x+x-3 = 2x-3
Therefore, the required equation would be;
2x-3 = 7.80
5.
We let the number of men be x, then the number of women would be x+6 since we are told that there were six more women on the committee than men. The total number of people on the committee in terms of x is thus;
x+x+6 = 2x+6
Therefore, our required equation would be;
2x+6 = 30
6.
Three consecutive integers have the sum of 153.
We let the three consecutive integers be;
x, x+1, and x+2
The difference between consecutive integers is usually 1.
The sum of the above integers in terms of x would be;
x+x+1+x+2 = 3x+3
Therefore, our required equation would be;
3x+3 = 153
7. Five times the first of three consecutive even integers is fourteen more than three times the second.
We let the first even integer be x. The second even integer would be x+2 while the third one would be x+4. The difference between two consecutive even integers is always 2. Now Five times the first of three consecutive even integers would be;
5*x = 5x
On the other hand, three times the second even integer would be;
3*(x+2) = 3x + 6
Now, we are told that 5x exceeds 3x + 6 by 14. Therefore, we can write;
5x - (3x +6) = 14
2x - 6 = 14
Which is the required equation
8. The sum of three consecutive even integers is fifty-four.
We let the first even integer be x. The second even integer would be x+2 while the third one would be x+4. The difference between two consecutive even integers is always 2. The sum of the three consecutive even integers in terms of x would be;
x+x+2+x+4 = 3x+6
The required equation would thus be;
3x + 6 = 54
9. An airplane flies at a rate of 356 km/h. The plane travels a total distance of 1424 km. (Use Distance = Rate * Time for your equation.)
The distance traveled by the plane is given as 1424 while its rate or speed is 356. We let t denote the time it took the plane to travel the given distance at the given rate. Using the equation Distance = Rate * Time, we can write the following equation in t;
1424 = 356*t
Which is our required equation.