Respuesta :
Answer: The correct answer is:
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" 5 [five] quarts of motor oil will cost:
→ " $ 4.72 " .
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First method of solving the problem:
Set up a ratio/proportion; in the form of an equation—using fractions— as follows:
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[tex]\frac{3qt}{2.83} = \frac{5 qt}{x}[/tex] ; → in which we are to solve for "x" {value in "dollars".}.
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Now, let's "cross-factor multiply" the values in the equation:
3*(x) = (2.83) * 5 ;
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Now, simplify—and rewrite the equation:
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3x = 14.15 ;
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Now, divide Each side of the equation by "3" ;
to isolation "x" on one side of the equation;
& to solve for "x" ;
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3x / 3 = (14.15) / 3 ;
to get: x = 4.71666666.... (dollars);
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Let us round that number up to: "4.72" ;
{since: "4.71" ; is followed by a digit higher than "4" } ;
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The correct answer is:
→ " 5 [five] quarts of motor oil will cost: " $ 4.72 " .
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Second method of solving this problem:
1) First: We treat this problem as a "unit rate" problem;
{that is; given a numeric quantity per certain numeric value;
→ we reduce/solve for what that Particular Quantity is,
per that particular [Single] Unit numeric value.
→ For this particular problem; we are given:
$ 2.83 ["2.83 dollars"] ; per " 3 quarts " ;
We began by reducing/solving this cost (in dollars);
→ "per quart" ; [i.e. per "one quart"] ;
[i.e. per "single, unit quart"] ;
So; " [tex]\frac{2.83 dollars}{3quarts} = (\frac{2.83}{3}) \frac{dollars}{quart}[/tex] " ;
= (2.83 ÷ 3) dollars/quart ;
= 0.94333333333............. dollars per quart.
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2) Second: Then: We take that value; and to find the cost of "5 (five) quarts" (as the problem asks)—we multiply that value by "5" :
→ Using calculator:
→ 0.943333333333333333333333.... * 5 ;
= 4.7166666666.. dollars ;
→ which is the same answer obtained from the first method.
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Third method of solving the problem:
This is really just an extension of the second method directed aforementioned:
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[tex]\frac{2.83 dollars}{3quarts} * \frac{5 quarts}{1} = ?[/tex] ;
→ The units of "quarts" cancel out; since: [" quarts/quarts = 1 "] ;
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and we have:
[tex]\frac{(2.83) *5}{3}[/tex] dollars ;
→ (2.83) * 5 = 14.15 ;
→ [tex]\frac{(2.83) *5}{3} = \frac{(14.15)}{3}[/tex] ;
= (14.15) ÷ 3 ; = 4.716666666666 ...
→ which is the same answer from the other 2 (two) aforementioned methods.
→ Let us round that number up to: "4.72" ;
{since: "4.71" ; is followed by a digit higher than "4" } ;
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So: The correct answer is:
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" 5 [five] quarts of motor oil will cost: $ 4.72 . "
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Hope this is helpful to you! Best of luck to you!
