2.3 Solve a Formula for a Specific Variable

Rearranging literal equations so any letter becomes the subject, and applying that skill to geometry formulas for area, perimeter, and volume.

Intermediate Algebra 2e, 2.3 Solve a Formula for a Specific Variable

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51 exercises

2.3 Exercise 1

Before you get started, take this readiness quiz.

Evaluate $2 \left(x + 3\right)$ when $x = 5 .$
If you missed this problem, review the reference.

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2.3 Exercise 2

The length of a rectangle is three less than the width. Let w represent the width. Write an expression for the length of the rectangle.
If you missed this problem, review the reference.

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2.3 Exercise 3

Evaluate $\frac{1}{2} b h$ when $b = 14$ and $h = 9 .$
If you missed this problem, review the reference.

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2.3 Exercise 5

Use the formula $A = \frac{1}{2} b h$ to solve for b.

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2.3 Exercise 6

Use the formula $A = \frac{1}{2} b h$ to solve for h.

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2.3 Exercise 8

Solve the formula $F = \frac{9}{5} C + 32$ for C.

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2.3 Exercise 9

Solve the formula $A = \frac{1}{2} h \left(b + B\right)$ for b.

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2.3 Exercise 11

Solve the formula $A = P + P r t$ for t.

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2.3 Exercise 12

Solve the formula $A = P + P r t$ for r.

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2.3 Exercise 14

Solve the formula $4 x + 7 y = 9$ for y.

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2.3 Exercise 15

Solve the formula $5 x + 8 y = 1$ for y.

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2.3 Exercise 17

The area of a triangular church window is 90 square meters. The base of the window is 15 meters. What is the window’s height?

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2.3 Exercise 18

A triangular tent door has an area of 15 square feet. The height is five feet. What is the length of the base?

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2.3 Exercise 20

The measure of one angle of a right triangle is 50 more than the measure of the smallest angle. Find the measures of all three angles.

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2.3 Exercise 21

The measure of one angle of a right triangle is 30 more than the measure of the smallest angle. Find the measures of all three angles.

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2.3 Exercise 26

The length of a rectangle is seven more than twice the width. The perimeter is 110 inches. Find the length and width.

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2.3 Exercise 27

The width of a rectangle is eight yards less than twice the length. The perimeter is 86 yards. Find the length and width.

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2.3 Exercise 29

One side of a triangle is seven inches more than the first side. The third side is four inches less than three times the first. The perimeter is 28 inches. Find the length of the three sides of the triangle.

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2.3 Exercise 30

One side of a triangle is three feet less than the first side. The third side is five feet less than twice the first. The perimeter is 20 feet. Find the length of the three sides of the triangle.

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2.3 Exercise 32

The perimeter of a rectangular swimming pool is 200 feet. The length is 40 feet more than the width. Find the length and width.

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2.3 Exercise 33

The length of a rectangular garden is 30 yards more than the width. The perimeter is 300 yards. Find the length and width.

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2.3 Exercise 37

Solve the given formula for the specified variable.

Solve the formula $C = \pi d$ for d.

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2.3 Exercise 39

Solve the given formula for the specified variable.

Solve the formula $V = L W H$ for L.

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2.3 Exercise 41

Solve the given formula for the specified variable.

Solve the formula $A = \frac{1}{2} b h$ for b.

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2.3 Exercise 43

Solve the given formula for the specified variable.

Solve the formula
$A = \frac{1}{2} d_{1} d_{2}$ for $d_{1} .$

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2.3 Exercise 45

Solve the given formula for the specified variable.

Solve the formula
$A = \frac{1}{2} h \left(b_{1} + b_{2}\right)$ for $b_{1} .$

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2.3 Exercise 47

Solve the given formula for the specified variable.

Solve the formula
$h = 54 t + \frac{1}{2} a t^{2}$ for a.

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2.3 Exercise 49

Solve the given formula for the specified variable.

Solve $180 = a + b + c$ for a.

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2.3 Exercise 51

Solve the given formula for the specified variable.

Solve the formula
$A = \frac{1}{2} p l + B$ for p.

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2.3 Exercise 53

Solve the given formula for the specified variable.

Solve the formula
$P = 2 L + 2 W$ for L.

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2.3 Exercise 55

Solve for the formula for y.

Solve the formula
$8 x + y = 15$ for y.

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2.3 Exercise 57

Solve for the formula for y.

Solve the formula
$−4 x + y = −6$ for y.

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2.3 Exercise 59

Solve for the formula for y.

Solve the formula
$x - y = −4$ for y.

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2.3 Exercise 61

Solve for the formula for y.

Solve the formula
$4 x + 3 y = 7$ for y.

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2.3 Exercise 63

Solve for the formula for y.

Solve the formula
$2 x + 3 y = 12$ for y.

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2.3 Exercise 65

Solve for the formula for y.

Solve the formula
$3 x - 2 y = 18$ for y.

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