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GrogVix [38]
3 years ago
10

Janet is painting her shed. She buys some gallon-sized paint cans that cost $15 each and 2 quart-sized paint cans that cost $4 e

ach. The cost of Janet's total purchase is $53. Write and solve an equation to determine the number of gallons of paint that Janet purchased.
Mathematics
1 answer:
blondinia [14]3 years ago
7 0

1 gallon cost $15

1 quarts cost $4

1 quarts = 1/4 gallon

15x for number of gallon cans

2 cans at $4 each = $8

15x + 8 = 53

Subtract 8 from both sides:

15x = 53-8

15x = 45

Divide both sides by 15:

x = 45/15

x = 3

She bought 3 gallon cans of paint

Plus she bought 2 quart cans, which is equal to a half gallon.

She bought a total of 3.5 gallons of paint.

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\huge \boxed{\mathbb{QUESTION} \downarrow}

  • How do you simplify this?
  • x²y+xy² / y²+2/5 × xy

\large \boxed{\mathbb{ANSWER\: WITH\: EXPLANATION} \downarrow}

\sf\frac{  { x  }^{ 2  }  y+x { y  }^{ 2  }    }{  { y  }^{ 2  }  + \frac{ 2  }{ 5  }   \times  xy  } \\

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_____

<u>How </u><u>to</u><u> factorise</u><u> </u><u>:</u><u>-</u>

<u>NUMERATOR</u> \downarrow

\sf \: x ^ { 2 } y + x y ^ { 2 }

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<u>DENOMINATOR</u> \downarrow

\sf{ y  }^{ 2  }  + \frac{ 2  }{ 5  }   \times  xy \\

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\sf \: {\frac{1}{5}y\left(2x+5y\right)}  \\

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Continuing...

\sf\frac{xy\left(x+y\right)}{\frac{1}{5}y\left(2x+5y\right)}  \\

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\sf\frac{x\left(x+y\right)}{\frac{1}{5}\left(2x+5y\right)}  \\

Expand the expression.

\sf\frac{x^{2}+xy}{\frac{2}{5}x+y}  \\

This can further simplified to as \downarrow

=    \boxed{\boxed{\bf\frac{5x\left(x  +y\right)}{2x+5y}}}

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