confusing word problems?

Question

i need some tutoring for my online algebra class

In the summer olympics, the US won 24 more gold medals
than the Germany team. if the total number of gold medals for both is 64 than find the number of gold medals that each team won


A 21-foot beam is to be divided so that the loinger peoce is 1 ft more than 3 times the shorter piece. if X represents the length of the shorter piece, find the lengths of both pieces

A plumer gave an estimate for the renovation of a kitchen. her hourly pay is $27 per hr. and the plumers parts will cost $80. if her total estimate is $404, how many hours does she expect this job to take.. (sentnce equation, please show equation)

Answer 1

let

x = germay gold medals

x + 24 = US gold metals

64 = Total gold metals

- - - - - - -

x + x + 24 = 64

2x + 24 = 64

2x + 24 - 24 = 64 - 24

2x = 40

2x/2 = 40 / 2

x = 40/2

x = 20

- - - - - -

The Germans had 20 gold Metals

The US has 44 gold Metals

- - - - - - - -s-

Answer 2

x is the number of medals by the German team
x+ 24 is the number of medals by the US team
x + x + 24 = 64
2x + 24 = 64
2x = 40
x = 20
x+ 24 = 20 + 24 = 44
US = 44
Germany = 20

x is the shorter piece
3x + 1 is the longer piece
x + 3x + 1 = 21
4x + 1 = 21
4x = 20
x = 5
3x + 1 = 3(5) + 1 = 15 + 1 = 16
The shorter piece is 5 ft. and the longer one is 16 ft.

H is number of hours
80 + 27H = 404
27H = 324
H = 12
the plumber is charging $12 per hour.

Answer 3

First Question:

US = 24 + Ger
US + Ger = 64

By substitution:

(24 + Ger) + Ger = 64
24 + 2Ger = 64
2Ger = 64 - 24
2Ger = 40
Ger = 20, therefore US = 44

Second Question:

Longer = 3X + 1
X + Longer = 21

By Substitution:

X + (3X + 1) = 21
4X + 1 = 21
4X = 21-1
4X = 20
X = 20/4
X = 5; therefore Longer = 16

Third Question:

Let x = no. of hours job expected to take

27x + 80 = 404
27x = 404 - 80
27x = 324
x = 324/27
x = 12 hours

Answer 4

US won 24 more than Germans, so
G + G+24 = 64
2G+24=64
2G=40
G=20
so Americans won 20 + 24 =44

3x+1+x=21
4x + 1 = 21
4x=20
x=5 so longer is 3(5)+1 = 16

Plummer
27x + 80 = 404
27x=324
x=12 hours

Answer 5

1.) (x+24) + x = 64

x = 44 for US .. germany had 20

2.) 3x + 1 + x =21
the longer beam is 16
the shorter beam is 5 ft

once u solve for the shorter beam put that number into the equation for the longer one. 3x + 1

3.) 404 - 80 = 316 / 27 = 11 19/27 so he'd need to work 12 hours if he could not have fractional hours

Answer 6

A.) use variables.
X for Germany golds
X+24 for US golds.
Now X + X + 24 =64
2x = 40
x = 20
germany won 20
US won 44

B.) same variable setup
X is the smaller piece
3x-1 is the bigger piece
and
x + 3x+1 = 21
4x=20
x=5
smaller piece is 5ft
larger piece is 16 ft

C.) 27h + 80 = 404
27h = 324
h=12
12 hours.