BRAINLIST AND 30 POINTS!
1. 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. Find 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 32.
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.

Question

06-02-2019
Mathematics

contestada

BRAINLIST AND 30 POINTS!
1. 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. Find 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 32.
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.

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mathstudent55 mathstudent55 · Answer 1 · 2019-02-06T19:53:50+01:00

1.b)

Fred has F cards. Bill has B cards. Tim has T cards.

B + F + T = 167

B = 5F

T = 4F - 3

5F + F + 4F - 3 = 167

10F - 3 = 167

10F = 170

F = 17

Fred has 17 cards.

B = 5F = 5(17) = 85

Bill has 85 cards.

T = 4F - 3 = 4(17) - 3 = 65

Tim has 65 cards.

2.a)

length = L

width = W

L = W + 5

perimeter = 2L + 2W = 168

2L + 2W = 168

2(W + 5) + 2W = 168

2W + 10 + 2W = 168

4W = 158

W = 39.5

L = W + 5 = 39.5 + 5 = 44.5

Length = 44.5 inches

Width = 39.5 inches

2.b)

Original rectangle:

width = W

length = 2W

New rectangle:

width = W - 1

length = 2W + 4

perimeter = 198 inches

perimeter = 2L + 2W = 198

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

4W + 8 + 2W - 2 = 198

6W + 6 = 198

6W = 192

W = 32

L = 2W = 64

width = 32 inches

length = 64 inches

3.a)

Now:

Sam's age = S

John's age = 3S

In 5 years:

John's age = 3S + 5

Sam's age = S + 5

3S + 5 = 2(S + 5)

3S + 5 = 2S + 10

S = 5

Sam's age is 5.

John's age is 15.

This is all I have time for now. Post the rest of the problems in a different post, and I'll try to help later.