# Thread: Mixed Questions: Help Needed

1. ## Mixed Questions: Help Needed

3 5/8 – ½ =
1¾ divided by 2 =

Write as a ratio in simplest form
a) 24:40 (would it be 3:5)
b) 220 cm to 1 m

Leah and Rachael both drive the same car, and use it basically at the same rate.
If Leah drives for 8 hours at 60 km/h to visit her best friend, the trip costs $63 in fuel. Rachael however drives to see her father but has to drive a further 256 km. How much will the trip cost in fuel? Three People contribute money to a raffle -$15, $20 and$25. If the winnings are distributed in same ratio as the contributions how much would each person get, if they won \$270?

2. Originally Posted by Quester
3 5/8 – ½ =
1¾ divided by 2 =

Write as a ratio in simplest form
a) 24:40 (would it be 3:5)
b) 220 cm to 1 m
For the first one convert the mixed numbers into improper fractions:
$3~\frac{5}{8} = \frac{29}{8}$

so
$3~\frac{5}{8} - \frac{1}{2} = \frac{29}{8} - \frac{1}{2}$

$= \frac{29}{8} - \frac{4}{8} = \frac{25}{8}$

If you really must have the answer as a mixed number, then
$\frac{25}{8} = 3 + \frac{1}{8} = 3~\frac{1}{8}$

The same thing goes for the other one.

For the ratios:
a) 24:40
$\frac{24}{40} = \frac{3 \cdot 8}{5 \cdot 8} = \frac{3}{5}$
and this is 3:5.

Again, the other one works the same way.

-Dan

3. Simplify (expand and collect like terms)
a)4q + 12q – 3
b)4 (3a + 1) + 2a
c)Subtract 3x – 5 from 8x – 18

Factorise Following
a)3a + 15 ( is it: 3a + 15 = 3 x a + 3 x 5 = 3(a+5)
b)4 x – xy + 3x2

Solve Following

a)2n + 3 = 17
b)3x – 4/2 – 6 = 4
c)5(x – 2) = 4 (x + 9)

But this particually, I can’t get:

a) The adjacent sides of a rectangle are (3x – 8) and 6 cm.
Given that the area of the rectangle is 96 cm^2, find the length of the rectangle and the value of x.

c)The Three sides of a triangle are 1/1 y + 2 and y = 4. The perimeter is 87 cm. What are the lengths of the three sides?

4. oh sorry when i wrote 1/2 i mean the fraction 1/2

5. Originally Posted by Quester
Simplify (expand and collect like terms)
a)4q + 12q – 3
b)4 (3a + 1) + 2a
c)Subtract 3x – 5 from 8x – 18

Factorise Following
a)3a + 15 ( is it: 3a + 15 = 3 x a + 3 x 5 = 3(a+5)
b)4 x – xy + 3x2

Solve Following

a)2n + 3 = 17
b)3x – 4/2 – 6 = 4
c)5(x – 2) = 4 (x + 9)

But this particually, I can’t get:

a) The adjacent sides of a rectangle are (3x – 8) and 6 cm.
Given that the area of the rectangle is 96 cm^2, find the length of the rectangle and the value of x.

c)The Three sides of a triangle are 1/1 y + 2 and y = 4. The perimeter is 87 cm. What are the lengths of the three sides?
1. Do yourself and do us a favor and start a new thread if you have new questions.

2. to #1.c.):
Translate the sentence into a mathematical operation:

$(8x-18)-(3x-5)~\buildrel {expand} \over \longrightarrow~8x-18-3x+5 = 5x-13$

to #2.a.): Yes
to 2.b.):
$4x - xy + 3x^2= x(4-y+3x)$

to #3.c.):

$5(x-2) = 4 (x + 9)~\iff~ 5x-10=4x+36~\iff~x=46$ ....... The last step is: add (-4x+10) on both sides of the equation - you only have to know why this is necessary!

to #4.a.):
You are suposed to know that the area of a rectangle is calculated by:

$area = length\ \cdot \ width$ ....... with
$length = 3x-8$ ....... and ....... $width = 6$

So you have to solve for x:

$(3x-8) \cdot 6 = 96 ~\iff~ 18x - 48 = 96~\iff~ 18x = 144 ~\iff~ x = \frac{144}{18} = 8$

Therefore the rectangle has the dimensions: $l = 16$ and $w = 6$

6. Originally Posted by earboth
So you have to solve for x:

$(3x-8) \cdot 6 = 96 ~\iff~ 18x - 48 = 96~\iff~ 18x = 144 ~\iff~ x = \frac{144}{18} = 8$

Therefore the rectangle has the dimensions: $l = 16$ and $w = 6$
how did you get the answer for (3x-8).6 = 96 what does the dot stand for?

7. Originally Posted by Quester
how did you get the answer for (3x-8).6 = 96 what does the dot stand for?
Multiplication