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Solve for the variable in each equation: a) 1/4x = 10, b) 2/3y = 8, d) 5/8t = 10, e) 7/12s = 14, g) 5/9m = 15

Mathematics

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6 parts
a

40\text{40}

b

12\text{12}

d

16\text{16}

e

24\text{24}

g

27\text{27}

h

30\text{30}

Step-by-step solution

17 steps

Here are the solutions for finding the value of the letter in each equation:

Part a· 2 steps

  1. Write the given equation.

    14x=10\frac{1}{4}x = 10

  2. Multiply both sides by 4 to isolate xx.

    4×14x=10×44 \times \frac{1}{4}x = 10 \times 4 x=40x = 40

    The value of xx is 40\boxed{\text{40}}.

Part b

12\text{12}

  1. Write the given equation.

    23y=8\frac{2}{3}y = 8

  2. Multiply both sides by the reciprocal of 23\frac{2}{3}, which is 32\frac{3}{2}.

    32×23y=8×32\frac{3}{2} \times \frac{2}{3}y = 8 \times \frac{3}{2}

  3. Simplify the multiplication.

    y=242y = \frac{24}{2} y=12y = 12

    The value of yy is 12\boxed{\text{12}}.

Part d

16\text{16}

  1. Write the given equation.

    58t=10\frac{5}{8}t = 10

  2. Multiply both sides by the reciprocal of 58\frac{5}{8}, which is 85\frac{8}{5}.

    85×58t=10×85\frac{8}{5} \times \frac{5}{8}t = 10 \times \frac{8}{5}

  3. Simplify the multiplication.

    t=805t = \frac{80}{5} t=16t = 16

    The value of tt is 16\boxed{\text{16}}.

Part e

24\text{24}

  1. Write the given equation.

    712s=14\frac{7}{12}s = 14

  2. Multiply both sides by the reciprocal of 712\frac{7}{12}, which is 127\frac{12}{7}.

    127×712s=14×127\frac{12}{7} \times \frac{7}{12}s = 14 \times \frac{12}{7}

  3. Simplify the multiplication.

    s=14×127s = \frac{14 \times 12}{7} s=2×12s = 2 \times 12 s=24s = 24

    The value of ss is 24\boxed{\text{24}}.

Part g

27\text{27}

  1. Write the given equation.

    59m=15\frac{5}{9}m = 15

  2. Multiply both sides by the reciprocal of 59\frac{5}{9}, which is 95\frac{9}{5}.

    95×59m=15×95\frac{9}{5} \times \frac{5}{9}m = 15 \times \frac{9}{5}

  3. Simplify the multiplication.

    m=15×95m = \frac{15 \times 9}{5} m=3×9m = 3 \times 9 m=27m = 27

    The value of mm is 27\boxed{\text{27}}.

Part h

30\text{30}

  1. Write the given equation.

    710n=21\frac{7}{10}n = 21

  2. Multiply both sides by the reciprocal of 710\frac{7}{10}, which is 107\frac{10}{7}.

    107×710n=21×107\frac{10}{7} \times \frac{7}{10}n = 21 \times \frac{10}{7}

  3. Simplify the multiplication.

    n=21×107n = \frac{21 \times 10}{7} n=3×10n = 3 \times 10 n=30n = 30

    The value of nn is 30\boxed{\text{30}}.

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