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

Let

x--------> the number of quarts of paint needed for the outside

y--------> the number of quarts of paint needed for the inside

we know that

$x=y+19$ ---------> equation $1$

$x+y=107$ ---------> equation $2$

Substitute  equation $1$ in equation $2$

$[y+19]+y=107$

$2y=107-19$

$2y=88$

$y=44\ quarts$

therefore

the answer is

$44\ quarts$ of paint for the inside  

Answer 2

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