MATH SOLVE

4 months ago

Q:
# One number is bigger than another by 406. If the bigger number is divided by the smaller one, you’ll get the quotient 3 and remainder 66. Find the numbers.

Accepted Solution

A:

The larger number is 576, the smaller number is 170.

Let x = the larger number and y = the smaller number.

We know that the larger number is 406 larger than the smaller one; therefore

x = y + 406

We also know

[tex]\frac{x}{y}=3\frac{66}{y}[/tex]

Substituting for x we have:

[tex]\frac{y+406}{y}=3+\frac{66}{y}[/tex]

When we convert mixed numbers to improper fractions, we multiply the whole number by the denominator and add the numerator:

[tex]\frac{y+406}{y}=\frac{3y+66}{y}[/tex]

Since the denominators are the same, we can just set the numerators equal

y+406=3y+66

We cannot have a variable on both sides, so we will subtract y from both sides:

y+406-y=3y+66-y

406=2y+66

Subtract 66 from both sides:

406-66=2y+66-66

340=2y

Divide both sides by 2:

340/2 = 2y/2

170=y

The smaller number is 170. Since the larger number is 406 larger, then it is 170+406=576.

Let x = the larger number and y = the smaller number.

We know that the larger number is 406 larger than the smaller one; therefore

x = y + 406

We also know

[tex]\frac{x}{y}=3\frac{66}{y}[/tex]

Substituting for x we have:

[tex]\frac{y+406}{y}=3+\frac{66}{y}[/tex]

When we convert mixed numbers to improper fractions, we multiply the whole number by the denominator and add the numerator:

[tex]\frac{y+406}{y}=\frac{3y+66}{y}[/tex]

Since the denominators are the same, we can just set the numerators equal

y+406=3y+66

We cannot have a variable on both sides, so we will subtract y from both sides:

y+406-y=3y+66-y

406=2y+66

Subtract 66 from both sides:

406-66=2y+66-66

340=2y

Divide both sides by 2:

340/2 = 2y/2

170=y

The smaller number is 170. Since the larger number is 406 larger, then it is 170+406=576.