Algebra,using equations questions-help

Question

1. James can do 2/5 as many weight lifts as Ted. If James can do 16 weight lifts, how many can Ted do?

2. Bill and Sonya spent $550 on a CD splayer but Sonya put in $60 less than Bill. How much did they each pay?

3. Given the volume of the following object, Find its height:

http://www.flickr.com/photos/99973477@N03/11444576954/

4. Sarah earns $400 a week plus $18 for each unit she sells.

a) write an equation for her weekly earnings. E= amount earned and U=number of units sold

b) how much would she earn if she sold 6 units in a week?

c) if she earned $544 in a week, how many units did she sell?

5. Using one of the 2 algebraic methods to solve the following.

a) Sam is 2 years older than Jan. If you add up their ages the anwser is 36. Find Sam's age and find Jan's age. Let J stand for Jan's age  and S stand for Sam's age

b) Ron is 5 years younger than Tom. If you add up their ages the answer is 33. How old is Ron and how old is Tom? Let T stand for Tom's age and R stand for Ron's age.

Answer 1

1) Ted can do weight lifts say = x

James can do 2/5 as many weight lifts as Ted,

James can do 2/5+x 

James can do 16 weight lifts

2/5+x = 16

Subtract 2/5 from each side.

2/5-2/5+x = 16-2/5

x = (80-2)/5

x = 78/5

Ted can do weight lifts = 78/5

2) Bill pay on a CD player say = $x

Sonya pay on a CD player = x-60

But Bill and Sonya spent = $550

x+x-60 = 550

2x-60 = 550

Add 60 to each side.

2x-60+60 = 550+60

2x = 610

Divide to each side by 2.

2x/2 = 610/2

x = 305

Bill pay on CD player $305.

Sonya pay on CD player = x-60 = 305-60 = $245

Answer 2

5) a) Age of the jan is say = x = J

Age of the sam is say = x+2 = S

According to given problem S+J = 36

x+x+2 = 36

2x+2 = 36

2x = 36-2

2x = 34

x = 34/2

x = 17

⇒ J = 17

⇒ S = 17+2 = 19

b)Age of Tom  say = x = T

Age of Ron = x-5 = R

According to given problem T+R = 33

x+x-5 = 33

2x-5 = 33

2x-5+5 = 33+5

2x = 38

2x/2 = 38/2

x = 19

T = 19

R = 19-5 = 14

 

 

Answer 3

3.

The given object is rectangular prism and its length is 4 cm, width is 3 cm, height is h cm and its volume is 90 cm³.

Calculate the volume of the rectangular prism by using formula : V = l * w * h, where l = length, w = width, h = height.

Substitute the values of l = 3, w = 3 and V = 90 in the above formula.

90 = 4 * 3 * h

90 = 12 * h

90/12 = h

h = 7.5 cm.

The height of the rectangular prism 7.5 cm.

Answer 4

4.

(a).

Let E represents the amount earned by Sarah and U represents the number of units sold by Sarah.

The cost of the one unit is $18.

The cost of the U unit is $18U.

The word " plus" represent the addition operation and its symbol is " + ".

The word " Earns $400 a week plus $18 for each units" represent the equation is E = 400 + 18U.

 

(b). The equation is E = 400 + 18U.

Substitute the value of U = 6 in the above equation.

E = 400 + 18(6)

E = $508.

Sarah earned for 6 units in a week is $508.

 

(c). The equation is E = 400 + 18U.

Substitute the value of E = $544 in the above equation.

(544) = 400 + 18U

144 = 18U

8 = U

Sarah sold the number of units in a week for $544 is 8.