I am trying to figure out how to write the equation to solve: the first number is 5 less than the second number. Four times the first number plus 5 times the second number is 74. Find the numbers

There are two numbers involved, let's call them x and y (x=first y=second).

Let's look at the information involved.

The first number is 5 less than the second.

So, X=Y-5.

Four times the first number plus 5 times the second number is 74.

So we can deal with just one variable, which will be Y, we can insert the expression y-5 for x.

So, the equation would look like:

4 (y-5) + 5Y=74

Let's solve.

We need to multiply the parenthesis first.

4y-20+5Y=74

Now add like terms.

9Y-20=74

We need Y by itself, so lets add 20 to both sides.

9Y=94

Let's divide.

10 4/9=Y

Since the first number is five less, it is 5 4/9. Let's check by putting it through the equation.

4 (5 4/9) + 5 (10 4/9) =

21 7/9+52 2/9

73+1=74

So the numbers are 5 4/9 and 10 4/9.