one number 4 more than another; if 6 times smaller minus....

[hmick72]

One number is 4 more than another. If 6 times the smaller minus 4 times the larger is 4, what are the two numbers:?

 

[stapel]

One number is 4 more than another. If 6 times the smaller minus 4 times the larger is 4, what are the two numbers:?

To begin, translate the exercise from English into math:

i) Pick a variable for the first, "smaller", number.

ii) Create an expression for the second, "larger", number, which is given as being four more than the first number, using the variable from (i).

iii) Create an expression, in terms of (i), for "six times the smaller".

iv) Create an expression, in terms of (ii), for "four times the larger".

v) Create an expression, in terms of (iii) and (iv), for "six times the first, minus four times the second".

vi) Note that "is" means "equals", and create an equation using (v) and the given result value.

vii) Solve the equation for the variable in (i).

viii) Back-solve for the value in (ii).

If you get stuck, please reply showing how far you have gotten in working through the steps. Thank you!

Eliz.

 

[black.lizzy]

Let us first assume the smaller number as x. Then the larger number is x+4 as it is 4 more than the smaller number.
I. x,x+4
Six times the smaller number is 6x
Four times the larger number is 4(x+4)
So according to the problem
6x-4(x+4)=4
6x-4x-16=4
2x=20
x=20/2=10
x+4=10+4=14
So the two numbers are 10 and 14