Question

divide 110 into two parts so that one will be 150 percent of the other?​

Answer 1

First, you must break down the problem into equations which you can solve. The method for doing this is known as solving by substitution:

The first equation you need defines the two parts of 110, x and y:

x + y = 110

The second equation defines the relationship that one part is 150% of the other:

x = y * 1.5

(150% is represented numerically as 1.5)

Now you must solve for one part, so we will choose x first. To do this you must remove the second component y from one of the equations. This will give you an equation with just x by itself. We are using the first equation to isolate y and the second equation to solve for x:

Take the first equation and get y by itself, giving you y in terms of x:

y = 110 - x

(Subtract x from both sides)

Now replace y in the second equation with that equivalent (this is the substitution part):

x = (110 - x) * 1.5

You can now solve for x:

x = 110*1.5 - 1.5x

(Multiply (110 - x) by 1.5 to simplify the right side of the equation)

x = 165 - 1.5x

(Add 1.5x to both sides of the equation to get x on the left side)

x + 1.5x = 165

(Add x and 1.5x)

2.5x = 165

(Divide both sides by 2.5 to get x by itself)

x = 165 / 2.5 = 66

Now that you have the value of x, plug it back in to the first equation, and solve for y:

66 + y = 110

(Subtract 66 from both sides)

y = 110 - 66 = 44

You have now solved the problem.

x = 66

y = 44

Check to be sure that x is 150% of y by calculating the following:

44 * 1.5 = 66

Finally, check to be sure that x and y add up to 110:

44 + 66 = 110

Answer 2

Answer:

First, you must break down the problem into equations which you can solve. The method for doing this is known as solving by substitution:

The first equation you need defines the two parts of 110, x and y:

x + y = 110

The second equation defines the relationship that one part is 150% of the other:

x = y * 1.5

(150% is represented numerically as 1.5)

Now you must solve for one part, so we will choose x first. To do this you must remove the second component y from one of the equations. This will give you an equation with just x by itself. We are using the first equation to isolate y and the second equation to solve for x:

Take the first equation and get y by itself, giving you y in terms of x:

y = 110 - x

(Subtract x from both sides)

Now replace y in the second equation with that equivalent (this is the substitution part):

x = (110 - x) * 1.5

You can now solve for x:

x = 110*1.5 - 1.5x

(Multiply (110 - x) by 1.5 to simplify the right side of the equation)

x = 165 - 1.5x

(Add 1.5x to both sides of the equation to get x on the left side)

x + 1.5x = 165

(Add x and 1.5x)

2.5x = 165

(Divide both sides by 2.5 to get x by itself)

x = 165 / 2.5 = 66

Now that you have the value of x, plug it back in to the first equation, and solve for y:

66 + y = 110

(Subtract 66 from both sides)

y = 110 - 66 = 44

You have now solved the problem.

x = 66

y = 44

Check to be sure that x is 150% of y by calculating the following:

44 * 1.5 = 66

Finally, check to be sure that x and y add up to 110:

44 + 66 = 110

Explanation:

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