At CVS, the tax paid was $2.45, which was 7% of the cost. What was the cost of the items purch

Mathematics

1 answer:

UNO [17]4 years ago

8 0

'Percentage' is obtained by multiplying 2.45 by - 7%.

- 7% × 2.45 =

(- 7 ÷ 100) × 2.45 =

(- 7 × 2.45) ÷ 100 =

- 17.15 ÷ 100 =

- 0.1715 ≈

- 0.17;

<h2>How do we check the result?</h2>

If - 7% × 2.45 = - 0.1715 =>

Divide - 0.1715 by 2.45...

... And see if we get as a result: - 7%.

100/100 = 100 ÷ 100 = 100% = 1

Multiply a number by the fraction 100/100,

... and its value doesn't change.

n/100 = n%, any number.

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9514 1404 393

Explanation:

When something is subtracted from both sides of the equation, the justification is the <em>subtraction property of equality</em>. When something multiplies both sides of the equation, the justification is the <em>multiplication property of equality</em>. (This should not be a mystery.)

Here, the equation is solved by subtracting 17/3, then subtracting 1/2x, then multiplying by the inverse of the coefficient of x. After each of these steps is a simplification.

$\begin{array}{cc}\dfrac{17}{3}-\dfrac{3}{4}x=\dfrac{1}{2}x+5&\text{given}\\\\\dfrac{17}{3}-\dfrac{3}{4}x-\dfrac{17}{3}=\dfrac{1}{2}x+5-\dfrac{17}{3}&\text{subtraction property ...}\\\\-\dfrac{3}{4}x=\dfrac{1}{2}x-\dfrac{2}{3}&\text{simplify}\\\\-\dfrac{3}{4}x-\dfrac{1}{2}x=\dfrac{1}{2}x-\dfrac{2}{3}-\dfrac{1}{2}x&\text{subtraction property ...} \end{array}$

$\begin{array}{cc}-\dfrac{5}{4}x=-\dfrac{2}{3}&\text{simplify}\\\\-\dfrac{5}{4}x\times-\dfrac{4}{5}=-\dfrac{2}{3}\times-\dfrac{4}{5}&\text{multiplication property ...}\\\\x=\dfrac{8}{15}&\text{simplify} \end{array}$