SOLUTION: seven more than the quotient of a number and 5 is the same as 42 i need to write it as an expression and solve it

Question 163683: seven more than the quotient of a number and 5 is the same as 42
i need to write it as an expression and solve it
Found 3 solutions by ankor@dixie-net.com, gonzo, Theo:
Answer by ankor@dixie-net.com(22740)   (Show Source): You can put this solution on YOUR website!
Just write what it says (x = "a number")
:
seven more than the quotient of a number and 5 is the same as 42
7 + = 42
:
= 42 - 7
:
= 35
:
x = 5(35)
:
x = 175
:
:
Check solution in original equation
7 + = 42
7 + 35 = 42
Answer by gonzo(654)   (Show Source): You can put this solution on YOUR website!
it appears that there are two unknowns here with one equation.
best you can do as far as i can tell is find a relationship between the two variables.
this is how i interpret the statement
-----
the statement is:
seven more than the quotient of a number and 5 is the same as 42.
if i let q = quotient of a number and 5, then q + 7 = 42 which results in
q = 35.
-----
quotient of a number and 5 means, to me, that if you divide a number + 5 by another number, the result is q.
so, letting y = that other number, that relationship shows up as
q = (x+5)/y
-----
if q = 35, then substituting (x+5)/y for q gets
(x+5)/y = 35
multiplying both sides of the equation by y gets
x+5 = 35*y
subtracting 5 from both sides of the equation gets
x = 35*y - 5
-----
that's the relationship.
-----
if y = 1, then x = 30
if y = 2, then x = 65
if y = 3, then x = 100
if y = 10, then x = 345
etc.
x can be any real number, and y can be any real number except 0 since it is used in the divisor. given a value of y, you will be able to solve for a value of x.
-----
to prove, let y = 25
original equation of q + 7 = 42
formula for q is
q = (x+5)/y
y = 25, so
q = (x+5)/25
-----
original equation is q+7 = 42
substituting for q gets
(x+5)/25 + 7 = 42
multiplying both sides of equation by 25 gets
(x+5) + 175 = 1050
(x+5) = 1050 - 175
x+5 = 875
x = 870
if y = 25, then x = 870.
-----
to prove that this is correct, we use the known value of y and the known value of x to substitute in the original equation.
y = 25
x = 870
equation is
(x+5)/y + 7 = 42
substituting 870 for x and 25 for y gets
(875/25 + 7 = 42
which becomes
35 + 7 = 42
which becomes 42 = 42
-----
based on the way the problem is stated, there is no value for x that works by itself.
you have to know y as well as x.
-----
that's my interpretation of the problem and my solution for it.
hopefully it's what you were looking for.
-----

Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
let x be the number.

this statement translates to x/5 + 7 = 42
subtract 7 from both sides of this equation to get x/5 = 35
multiply both sides of this equation by 5 to get x = 5*35 = 175
that's your answer.

the quotient of 175 and 5 is equal to 175/5 = 35
7 more than that equals 35 + 7 = 42

here's a reference that might help you translate verbal expressions into equation form.

http://www.delmar.edu/math/MLC/Forms/Translating_Verbal_Expressions.pdf
RELATED QUESTIONS
seven times a number is the same as 12 more than 3 times the number. Find the number. we... (answered by piglet162431)
My sons homework question, i need help... write the sentence as an equation, then solve... (answered by Fombitz)
I need to know how to write these following sentences into equations. 1.Eight times a... (answered by ikleyn)
write the phrase "89 more than the quotient of d and 21" as an algebraic... (answered by orca)
Help...I need to find A Number Such That Seven Times 1 Less Than Twice The Number Is The... (answered by ankor@dixie-net.com)
seven more than the quotient of a number b and 45 is greater than... (answered by MathLover1)
Seven plus the quotient of a number and 5 is -12. Write and solve the... (answered by MathLover1)
Twice the sum of a number and seven is three times the number. I need to write this as (answered by ikleyn)
A certain number, x, is doubled and then decreased by 11. The result is equal to the... (answered by jsmallt9)