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Sagot :
Let's break down each statement and write the corresponding equation, and then solve each equation step-by-step for the respective variable.
(i) The sum of numbers [tex]\(x\)[/tex] and 4 is 9.
[tex]\[ x + 4 = 9 \][/tex]
Subtract 4 from both sides:
[tex]\[ x = 9 - 4 = 5 \][/tex]
(ii) 2 subtracted from [tex]\(y\)[/tex] is 8.
[tex]\[ y - 2 = 8 \][/tex]
Add 2 to both sides:
[tex]\[ y = 8 + 2 = 10 \][/tex]
(iii) Ten times [tex]\(a\)[/tex] is 70.
[tex]\[ 10a = 70 \][/tex]
Divide both sides by 10:
[tex]\[ a = \frac{70}{10} = 7.0 \][/tex]
(iv) The number [tex]\(b\)[/tex] divided by 5 gives 6.
[tex]\[ \frac{b}{5} = 6 \][/tex]
Multiply both sides by 5:
[tex]\[ b = 6 \times 5 = 30 \][/tex]
(v) Three-fourth of [tex]\(t\)[/tex] is 15.
[tex]\[ \frac{3}{4}t = 15 \][/tex]
Multiply both sides by [tex]\(\frac{4}{3}\)[/tex]:
[tex]\[ t = 15 \times \frac{4}{3} = 20.0 \][/tex]
(vi) Seven times [tex]\(m\)[/tex] plus 7 gets you 77.
[tex]\[ 7m + 7 = 77 \][/tex]
Subtract 7 from both sides:
[tex]\[ 7m = 77 - 7 = 70 \][/tex]
Divide both sides by 7:
[tex]\[ m = \frac{70}{7} = 10.0 \][/tex]
(vii) One-fourth of a number [tex]\(x\)[/tex] minus 4 gives 4.
[tex]\[ \frac{1}{4}x - 4 = 4 \][/tex]
Add 4 to both sides:
[tex]\[ \frac{1}{4}x = 4 + 4 = 8 \][/tex]
Multiply both sides by 4:
[tex]\[ x = 8 \times 4 = 32 \][/tex]
(viii) If you take away 6 from 6 times [tex]\(y\)[/tex], you get 60.
[tex]\[ 6y - 6 = 60 \][/tex]
Add 6 to both sides:
[tex]\[ 6y = 60 + 6 = 66 \][/tex]
Divide both sides by 6:
[tex]\[ y = \frac{66}{6} = 11.0 \][/tex]
(ix) If you add 3 to one-third of [tex]\(z\)[/tex], you get 30.
[tex]\[ \frac{1}{3}z + 3 = 30 \][/tex]
Subtract 3 from both sides:
[tex]\[ \frac{1}{3}z = 30 - 3 = 27 \][/tex]
Multiply both sides by 3:
[tex]\[ z = 27 \times 3 = 81 \][/tex]
Thus, the solutions are:
[tex]\[ (x_1 = 5, y_1 = 10, a = 7.0, b = 30, t = 20.0, m = 10.0, x_2 = 32, y_2 = 11.0, z = 81) \][/tex]
(i) The sum of numbers [tex]\(x\)[/tex] and 4 is 9.
[tex]\[ x + 4 = 9 \][/tex]
Subtract 4 from both sides:
[tex]\[ x = 9 - 4 = 5 \][/tex]
(ii) 2 subtracted from [tex]\(y\)[/tex] is 8.
[tex]\[ y - 2 = 8 \][/tex]
Add 2 to both sides:
[tex]\[ y = 8 + 2 = 10 \][/tex]
(iii) Ten times [tex]\(a\)[/tex] is 70.
[tex]\[ 10a = 70 \][/tex]
Divide both sides by 10:
[tex]\[ a = \frac{70}{10} = 7.0 \][/tex]
(iv) The number [tex]\(b\)[/tex] divided by 5 gives 6.
[tex]\[ \frac{b}{5} = 6 \][/tex]
Multiply both sides by 5:
[tex]\[ b = 6 \times 5 = 30 \][/tex]
(v) Three-fourth of [tex]\(t\)[/tex] is 15.
[tex]\[ \frac{3}{4}t = 15 \][/tex]
Multiply both sides by [tex]\(\frac{4}{3}\)[/tex]:
[tex]\[ t = 15 \times \frac{4}{3} = 20.0 \][/tex]
(vi) Seven times [tex]\(m\)[/tex] plus 7 gets you 77.
[tex]\[ 7m + 7 = 77 \][/tex]
Subtract 7 from both sides:
[tex]\[ 7m = 77 - 7 = 70 \][/tex]
Divide both sides by 7:
[tex]\[ m = \frac{70}{7} = 10.0 \][/tex]
(vii) One-fourth of a number [tex]\(x\)[/tex] minus 4 gives 4.
[tex]\[ \frac{1}{4}x - 4 = 4 \][/tex]
Add 4 to both sides:
[tex]\[ \frac{1}{4}x = 4 + 4 = 8 \][/tex]
Multiply both sides by 4:
[tex]\[ x = 8 \times 4 = 32 \][/tex]
(viii) If you take away 6 from 6 times [tex]\(y\)[/tex], you get 60.
[tex]\[ 6y - 6 = 60 \][/tex]
Add 6 to both sides:
[tex]\[ 6y = 60 + 6 = 66 \][/tex]
Divide both sides by 6:
[tex]\[ y = \frac{66}{6} = 11.0 \][/tex]
(ix) If you add 3 to one-third of [tex]\(z\)[/tex], you get 30.
[tex]\[ \frac{1}{3}z + 3 = 30 \][/tex]
Subtract 3 from both sides:
[tex]\[ \frac{1}{3}z = 30 - 3 = 27 \][/tex]
Multiply both sides by 3:
[tex]\[ z = 27 \times 3 = 81 \][/tex]
Thus, the solutions are:
[tex]\[ (x_1 = 5, y_1 = 10, a = 7.0, b = 30, t = 20.0, m = 10.0, x_2 = 32, y_2 = 11.0, z = 81) \][/tex]
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