Question

Jay needs 19 quarts more paint for the outside of his barn then for the inside.if he uses 107 quarts in all,how many gallons of paint will be used to paint the inside of the barn?

Answer 1

There will be $\large{\boxed{\bold11}}}$ gallons to paint the inside of the barn

Further Explanation

One variable linear equation is an equation that has a variable and the exponent number is one.

Can be stated in the form:

 $\large{\boxed{\bold{ax=b}}}$

or

ax + b = c,

where a, b, and c are constants, x is a variable

Whereas the two-variable linear equation is a linear equation that has 2 variables and the exponent is one

Can be stated in the form:

 $\large{\boxed{\bold{ax+by=c}}}$

x, y = variable

Known

Jay needs 19 quarts more paint for the outside of his barn then for the inside

he uses 107 quarts in all

Asked

gallons of paint  used to paint the inside of the barn

Answer

let x = amount of quarts to paint inside

and 19+ x = amount of quarts to paint outside

If we translate this task sentence into equation

$\large{\boxed{(19+x)+x=107~quarts}}}$

This equation belongs to One variable linear equation  because there is one variable = x and the exponent number is one

solving equations :

$\displaystyle 19+2x=107~quartz$

$2x=107-19$

$2x=88$

x= 44 quartz

The units for US standart volume are :

• Fluid Ounces

• Cups
• Pints
• Quarts
• Gallons

The conversion for all those units :

1 gallon = 4 quarts = 8 pints = 16 cups = 128 fluid ounces

so conversions for 44 quarts to gallons :

1 gallon = 4 quarts

1 quarts = 0.25 gallons

$\displaystyle 44~quarts=44\times0.25~gallons$

$\displaystyle 44~quarts=\large{\boxed{\bold{11~gallons}}}$

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Keywords: paint, quarts, gallon

Answer 2

The question presents the relationship between the amount of paint to be

used for the inside of the barn and the amount of paint needed for the

outside in the form of a word problem.

• The amount of paint used to paint the inside of the barn is 11 gallons

Reasons:

Given parameter are;

The amount of more paint Jay needs to paint the outside of his barn = 19

quarts.

The amount of paint he uses in all = 107 quarts

Let I represent the amount of paint Jay needs to paint the inside of his

barn, we have;

The amount of paint Jay needs to paint his outside of his barn = I + 19

Therefore, we have;

The paint needed in all, 107 = Paint needed inside + Paint needed outside

Paint needed inside = I

Paint needed outside = I + 19

Therefore;

107 = I + I + 19 = 2·I + 19

107 - 19 = 2·I + 19 - 19

88 = 2·I

2·I = 88 by symmetric property of equality

$I = \dfrac{88}{2} = 44$

The amount of paint that will be used to paint the inside of the barn, I = 44

quarts.

4 quarts = 1 gallon

Therefore;

44 quarts = 4 quarts × 11 = 1 gallon × 11 = 11 gallons

• The number of gallons of paint that will be used to paint the inside of the barn is 11 gallons of paint.

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