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Express the following ratios as (A) fraction (B) Decimal (C) percentage

Mathematics

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Step-by-step solution

11 steps

Engineer, let's get these done.

Part 1

Express the following ratios as (A) fraction, (B) decimal, and (C) percentage.

  • 1) Ratio 2:5

    • A) Fraction: 25\boxed{\frac{2}{5}}
    • B) Decimal: 25=0.4\frac{2}{5} = \boxed{0.4}
    • C) Percentage: 0.4×100%=40%0.4 \times 100\% = \boxed{40\%}
  • 2) Ratio 4:12

    • A) Fraction: 412=13\frac{4}{12} = \boxed{\frac{1}{3}}
    • B) Decimal: 13≈0.3333\frac{1}{3} \approx \boxed{0.3333}
    • C) Percentage: 13×100%≈33.33%\frac{1}{3} \times 100\% \approx \boxed{33.33\%}
  • 3) Ratio 10:25

    • A) Fraction: 1025=25\frac{10}{25} = \boxed{\frac{2}{5}}
    • B) Decimal: 1025=0.4\frac{10}{25} = \boxed{0.4}
    • C) Percentage: 0.4×100%=40%0.4 \times 100\% = \boxed{40\%}

Part 2· 6 steps

Find the missing ratio from the equations below.

  • A) 3:5=15:X3:5 = 15:X
  1. Write the ratios as a proportion.

    $$
    \frac{3}{5} = \frac{15}{X}
    $$
    
  2. Cross-multiply to solve for XX.

    $$
    3X = 5 \times 15
    $$
    $$
    3X = 75
    $$
    
  3. Divide by 3.

    $$
    X = \frac{75}{3}
    $$
    $$
    X = \boxed{25}
    $$
    
    • B) 2:7=Y:562:7 = Y:56
  4. Write the ratios as a proportion.

    $$
    \frac{2}{7} = \frac{Y}{56}
    $$
    
  5. Cross-multiply to solve for YY.

    $$
    7Y = 2 \times 56
    $$
    $$
    7Y = 112
    $$
    
  6. 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.
  1. Simplify the ratio of the cost of a pen to a pencil.

    $$
    \text{Cost of Pen} : \text{Cost of Pencil} = 15:25 = 3:5
    $$
    
  2. Let the cost of a pen be 3k3k and the cost of a pencil be 5k5k, where kk is a constant.

    Calculate the cost of 5 pens and 3 pencils. Cost of 5 pens=5×(3k)=15k \text{Cost of 5 pens} = 5 \times (3k) = 15k Cost of 3 pencils=3×(5k)=15k \text{Cost of 3 pencils} = 3 \times (5k) = 15k

  3. 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.
  4. Use the simplified ratio of the cost of a pen to a pencil.

    $$
    \frac{\text{Cost of Pen}}{\text{Cost of Pencil}} = \frac{3}{5}
    $$
    
  5. Convert the fraction to a percentage.

    $$
    \frac{3}{5} \times 100\% = 0.6 \times 100\% = \boxed{60\%}
    $$
    
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