I need some math help?

Question

Solve the following problems:

1.

a) On Wednesday, Harry sold 3 times as many candy bars as on Tuesday. On Thursday, he sold 5 times as many bars as on Wednesday. He sold a total of 152 candy bars. How many did he sell each day?

b) Bill has 5 times as many baseball cards as Fred. Tim has 3 fewer than 4 times as many baseball cards as Fred. In all they have 167 baseball cards. How many does each have?

2.

a) The length of a rectangle is 5 more than the width. The perimeter of the rectangle is 168 inches. Find the dimensions of the rectangle.

b) The length of a rectangle is twice the width. If the length is increased by 4 inches and the width is diminished by 1 inch, a new rectangle is formed whose perimeter is 198 inches. Fine the dimensions of the original rectangle.

3.

a) John is now 3 times as old as his brother Sam. In 5 years, John will be twice as old as Sam will be then. Find their present ages.

b) Find four consecutive integers such that the sum of the second and the fourth is 132.

4.

a) Find four consecutive even integers such that twice the sum of the second and third exceeds 3 times the first by 34.

b) The difference between two numbers is 24. Find the numbers if their sum is 88.

5.

a) Separate 60 into two parts so that 3 times the smaller added to 6 more than 6 times the smaller = 60.

b) A train traveled 300 miles. How long did the trip take if the train was traveling at a rate of:

Note * Use the d=rt formula (distance = rate * time). NOTE: You may not be able to solve for the variable. If you do not have enough information to solve for the variable then write the equation.

(1) 50 mph (2) 70 mph (3) x mph

(4) (x + 10)mph (5) (x - 5)mph

*THANKS IN ADVANCE*

Answer 1

Favorite Answer

1-

a:

Let's assume the amount he sold on Tuesday is x , that means Wednesday is 3x and Thursday is 3x*5 = 15x.

If the total amount of a candy he sold is 152 we can solve for x

x+3x+15x=152

19x=152

Divide both sides by 19

x=8

That means he sold 8 candies On Tuesday,24 on Wednesday,120 on Thursday

Add those up

8+24=120=152

The answer is correct

------------------------------------------------------------------------------------------------------------------------------ b: Assuming Fred has x baseball cards , Bill has 5x baseball cards , and Tim has 4x-3 baseball cards

If the total amount of baseball cards is 167 we can solve for x

x+5x+4x-3=167

10x-3=167

We move 3 to the right hand side of the equation

10x=170

We divide both sides by 10

x=17

That means Fred has 17 Baseball cards , Bill 85 . and Tim 65

We add those up

17+85+65=167

The answer is correct

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2-

a:

Let the width be x , Therefore the length is 5x

If the parameter is 168 inches we can solve for x

2(x+5x)=168

We distribute 2 (Distributive property)

2x+10x=168

12x=168

We divide both sides by 12

x=14

That means the width of the rectangle is 14 and the length is 70.

Checking

(14+70)*2=84*2=168

The answer is correct

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b:

Let the width be x , Therefore the length is 2x

We know if we increase the length by 4 inches and decrease the width by 1 inch the parameter is 198 inches

We can solve for x

2((x-1)+(2x+4))=198

2(3x-3)= 198

Distributing 2

6x-6=198

We move 6 to the right hand side of the equation

6x=204

We divide both sides by 6

x=34

That means the original width is 34 inches , and the original length is 68 inches

Now we can calculate the original parameter

2(34+68)

2(102)=204

The original parameter is 204 inches

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3-

To solve this problem we need to solve a system of equations

a:

Let Sam's age be S , and John's age J , Therefore J=3S

That means

J=3S

(J+5)=2(S+5)

Substitute J with 3S

3S+5=2S+10

Move 5 to right hand side of the equation and 2S to the left hand side of the equation

S=5

Sam's current age is 5 years Therefore John's current age is 15

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b:

Let the first integer be x that means

(x+1)+(x+3)=132

2x+4=132

We move 4 to the right hand side of the equation

2x=128

We divide by 2

x=64

That means the integers are 64.65.66.67

Let's check

65+67=132

The answer is correct

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4:

a

Let the first integer be x . Therefore

2((x+1)+(x+2)=3x-34

2(2x+3)=3x-34

Distribute 2

4x+6=3x-34

Move 6 to the right hand side of the equation and 3x to the left hand side of the equation

x=-40

This means the integers are : -40,-39,-38,-37

Checking

2(-39-38)=3(-40)-34

2(-77)=3(-40)-34

154=120-34

154=154

The answer is correct

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b:

Let the 2 numbers be x,y

This means

x-y=24

x+y=88

We add the equations

2x=112

We divide both sides by 2

x=56

We now know the value of x ,therefore we can calculate y

56+y=88

We move 56 to the right hand side of the equation

y=32

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5-

a:

Let the small part be x . Therefore

3x+6x+6=60

9x+6=60

We move 6 to the right hand side of the equation

9x=54

We divide both sides by 9

x=6

if the small part is 6 that means the large part is :

y=60-x

=60-6=54

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b:

1-

d=rt

300=50t

Divide both sides by 50

t=6 hours

2- d=rt

300=70t

Divide both sides by 70

t ≈ 4.29 hours

3- d=rt

300=xt

We divide both sides by x

t=300/x

4- d=rt

300=(x+10)t

Divide both sides by (x+10)

t= 300/(x+10)

5- d=rt

300=(x-5)t

Divide both sides by (x-5)

t=300/(x-5)

Hope this helped :)

Answer 2

1) a) 3x + x + 5 (3x) = 152

3x + x + 15x = 152

19x = 152

x = 152/19

x = 8

tuesday --> 8

wednesday --> 8*3 = 24

thursday --> 8*15 = 120

b) 5x + x + (4x - 3) = 167

5x + x + 4x - 3 = 167

10x = 167 + 3

x = 170/10

x = 17

fred --> 17

bill --> 17*5 = 85

tim --> (17*4) - 3 = 65

2)a) 5x + x = 168

6x = 168

x= 168/6

x = 28

width = 28

length = 28*5 = 140

b) 198 - 4 - 4 + 1 + 1 = 192

2x + x = 192

3x = 192

x = 192/3

x = 64

width = 64

length = 64*2 = 128

Source(s): sorry, i couldn't go further than this. i hope this helped anyway :)