# Math Help - Some word problems need equation cracking =(

1. ## Some word problems need equation cracking =(

Hiya...

I got some word problems but I can't crack open the equation...can someone help?

2. Find three consecutive numbers such that twice the smallest is 23 more than the largest.

4. A scalene triangle has a perimeter of 36 cm. One side of this triangle is 3cm longer than the shortest side and the longest side is one cm more than twice the smallest side. Find the length of each side.

5. A father is now three times as old as his son. Eight years ago the father's age was five times that of his son. Find their present ages.

9. Two boys on bicycles start toward each other at the same time from two towns 70 km apart. The first travels at 12km/h. What is the speed of the other boy if both of them meet in 2 and a half hours?

12. The perimeter of a rectangle is 40cm. The length is 2cm more than 5 times the width. What are the dimensions of this rectangle?

13. Divide 556 into two parts such that if the larger part is added to 12 and the smaller part is added to 18 the resulting sums will be equal

I tried a couple of times but the answers that I got didn't make any sense at all o_O. So help would be greatly appreciated. Please DO NOT post the answers, please. I am only looking for equations and the rest I can do myself . Thanks! I find this forum really helpful. Thank you guys.

2. I only scanned a few problems but I think most of these problems can be solved just by using algebra.

For example, in question one you have three consecutive numbers, so you can call them n, n+1, and n+2. Then, if you put it into context you come up with the equation

2n = (n+2) + 23

Look for key words (for example, "is" usually corresponds to an equals sign) in the equation, and just look at your equation and make sure it makes sense.

3. Originally Posted by nathan02079
4. A scalene triangle has a perimeter of 36 cm. One side of this triangle is 3cm longer than the shortest side and the longest side is one cm more than twice the smallest side. Find the length of each side.
Let $x,y,z$ be the sides of the triangle, $x\leq y\leq z$.
We have: $x+y+z=36$ (1)
$y=x+3$ (2)
$z=2x+1$ (3)

Now, plug y and z in (1): $x+(x+3)+(2x+1)=36\Rightarrow 4x=32\Rightarrow x=8$

Plug x in (2) and (3): $y=11, \ z=17$

4. Originally Posted by nathan02079
5. A father is now three times as old as his son. Eight years ago the father's age was five times that of his son. Find their present ages.
Let $x$ be the age of the father and $y$ the age of the son.

We have: $x=3y$ (1)
8 years ago: $x-8=5(y-8)$ (2)
Plug x in (2): $3y-8=5(y-8)$ and solve for y.
Then plug y in (1) and find x.

5. Originally Posted by nathan02079
12. The perimeter of a rectangle is 40cm. The length is 2cm more than 5 times the width. What are the dimensions of this rectangle?

Let $x$ be the length and $y$ the width of rectangle.
The perimeter is $2x+2y=40$
and $x=5y+2$.

Now, solve for x and y.

6. Originally Posted by nathan02079
13. Divide 556 into two parts such that if the larger part is added to 12 and the smaller part is added to 18 the resulting sums will be equal

Let $x,y$ be the two parts, $x>y$.
Then we have the system:
$\displaystyle\left\{\begin{array}{ll}x+y=556\\x+12 =y+18\end{array}\right.$

Now, solve for x and y.

7. Originally Posted by nathan02079
Hiya...

...
9. Two boys on bicycles start toward each other at the same time from two towns 70 km apart. The first travels at 12km/h. What is the speed of the other boy if both of them meet in 2 and a half hours?

...
Hello,

the first boy travelled a distance of:

$d_1=12\ \frac{km}{h} \cdot \frac52\ h = 30\ km$

During the same time the 2nd boy has to travel

$d_2 = 70 - d_1 = 40\ km$

So his speed is:

$v_2=\frac{40\ km}{\frac52\ h}= 16\ \frac{km}{h}$