SOLUTION: 1. I think of two consecutive odd numbers. 5 times the smaller plus 3 timesthe larger is 62. find the two numbers. 2. Two numbers differ by 5. Seven times the smaller plus 4 tim

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Question 133594: 1. I think of two consecutive odd numbers. 5 times the smaller plus 3 timesthe larger is 62. find the two numbers.
2. Two numbers differ by 5. Seven times the smaller plus 4 times the larger is 108. find the numbers.
3. Find three consecutive odd numbers that have a sum of 57.
4. I write down 3 consecutive even numbers. 6 times the smallest plus 2 times the largest equals seven times the middle number. Find the three numbers.
5. When soe cards are dealt to six people, each receives three more than when the same cards are dealt to eight people. how many cards are there?
6. John is 'x' years old. his sister mary is 3 year older than john is.
a)write an expression for the sum of their ages
b)the diferrence between their ages. if 4 times the sum of their ages didvided by 20 is equal to difference between their ages, find both jons and mary's ages.
These six example questions that im having problem with i hope you could exlplain every single one for me thans in advance..
Found 2 solutions by checkley71, ankor@dixie-net.com:
Answer by checkley71(8403) (Show Source):
You can put this solution on YOUR website!
X & X+2 ARE THE 2 CONSECUTIVE ODD NUMBERS.
5X+3(X+2)=62
5X+3X+6=62
8X=62-6
8X=56
X=56/8
X=7 FOR THE SMALLER ODD NUMBER.
7+2=9 IS THE LARGER ODD NUMBER.
PROOF
5*7+3*9=62
35+27=62
62=62
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7X+4(X+5)=108
7X+4X+20=108
11X=108-20
11X=88
X=88/11
X=8 ANSWER FOR THE SMALLER NUMBER.
8+5=13 FOR THE LARGER NUMBER.
PROOF
7*8+4*13=108
56+52=108
108=108
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X+X+1+X+2=57
3X+3=57
3X=57-3
3X=54
X=54/3
X=18 ANSWER FOR THE SMALLER NUMBER.
18=1=19 THE NEXT NUMBER.
18+2=20 THE LARGER NUMBER.
PROOF.
18+19+20=57
57=57
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I'LL END HERE AS WE ARE TUTORS NOT HOMEWORK SOLVERS.

Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website!
:
4. I write down 3 consecutive even numbers. Find the three numbers.
3 consecutive even numbers: x, (x+2), (x+4)
:
"6 times the smallest plus 2 times the largest equals seven times the middle number." Solve for x:
6x + 2(x+4) = 7(x+2)
:
5. When some cards are dealt to six people, each receives three more than when the same cards are dealt to eight people. how many cards are there?
Let x = number of cards
:
= + 3
Multiply equation by 48:
48() = 48() + 48(3)
8x = 6x + 144
8x - 6x = 144
2x = 144
x = 72 cards
:
:
6. John is 'x' years old. his sister mary is 3 year older than john is.
a)write an expression for the sum of their ages
x = J's age; (x+3) = M's age
x + (x+3) = 2x + 3
:
b)the difference between their ages. if 4 times the sum of their ages divided by 20 is equal to difference between their ages, find both jons and mary's ages.
= 3
Multiply equation by 20 to get rid of the denominator
4(2x + 3) = 60
8x + 12 = 60
8x = 60 - 12
8x = 48
x = 48/8
x = 6 J's age; 9 = M's age