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Express the following ratios as (A) fraction (B) Decimal (C) percentage
Mathematics
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Step-by-step solution
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Part 1
Express the following ratios as (A) fraction, (B) decimal, and (C) percentage.
-
1) Ratio 2:5
- A) Fraction:
- B) Decimal:
- C) Percentage:
-
2) Ratio 4:12
- A) Fraction:
- B) Decimal:
- C) Percentage:
-
3) Ratio 10:25
- A) Fraction:
- B) Decimal:
- C) Percentage:
Part 2· 6 steps
Find the missing ratio from the equations below.
- A)
Write the ratios as a proportion.
$$ \frac{3}{5} = \frac{15}{X} $$Cross-multiply to solve for .
$$ 3X = 5 \times 15 $$ $$ 3X = 75 $$Divide by 3.
$$ X = \frac{75}{3} $$ $$ X = \boxed{25} $$- B)
Write the ratios as a proportion.
$$ \frac{2}{7} = \frac{Y}{56} $$Cross-multiply to solve for .
$$ 7Y = 2 \times 56 $$ $$ 7Y = 112 $$Divide by 7.
$$ Y = \frac{112}{7} $$ $$ Y = \boxed{16} $$
Part 3· 5 steps
The cost of a pen to a pencil is 15:25.
- A) Find the total cost of 5 pens and 3 pencils.
Simplify the ratio of the cost of a pen to a pencil.
$$ \text{Cost of Pen} : \text{Cost of Pencil} = 15:25 = 3:5 $$Let the cost of a pen be and the cost of a pencil be , where is a constant.
Calculate the cost of 5 pens and 3 pencils.
Calculate the total cost.
$$ \text{Total Cost} = 15k + 15k = \boxed{30k} $$ (Note: The question does not provide a specific value for the total cost, so the answer is expressed in terms of $k$.)- B) Express the Cost of a Pen to a Pencil as a Percentage.
Use the simplified ratio of the cost of a pen to a pencil.
$$ \frac{\text{Cost of Pen}}{\text{Cost of Pencil}} = \frac{3}{5} $$Convert the fraction to a percentage.
$$ \frac{3}{5} \times 100\% = 0.6 \times 100\% = \boxed{60\%} $$
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