Formulae and Linear Equations in Two Variables

Question 1

The difference between four times a number and 12 is 55. Find the number.

Answer 1

17

Question 2

The sum of the two numbers is 21. Three times the larger is equal to four times the smaller. Find them

Answer 2

12

Question 3

The sum of three consecutive odd integers is fifty-one. Find them.

Answer 3

15, 17 and 19

Question 4

A child has $11.35 in his piggy bank in nickels, dimes, and quarters. How many each does he have if the number of his dimes is half the number of his nickels and the number of quarters is 5 less than the number of his dimes?

Answer 4

56 nickels, 28 dimes and 23 quarters

Question 5

V = πr²h
if V = 14.75 and r = 2.1 find h

Answer 5

h = 1.065

Question 6

a = √(b² + c²)
if c = -15 and b = -20
solve for a

Answer 6

a = 25

Question 7

g) a² = b² + c²
if b = 3 and c =4
solve for a

Answer 7

a = ±5

Question 8

C = a - 2(A/b)
if a = -2, A = 3 and b =7
solve for C

Answer 8

-2.86

Question 9

K = 0.5h(a + b)
if K = 48, a = 5 and b = 7
solve for h

Answer 9

h = 8

Question 10

Solve: P = a + b + c
for b

Answer 10

b = P - a - c

Question 11

Solve: P = 2l + 2w for w

Answer 11

w = (P - 2l)/2

Question 12

Solve: V = lwh for h

Answer 12

h = V/ lw

Question 13

Solve: y = 1/2(x + z) for x

Answer 13

x = 2y - z

Question 14

Solve: A = P(1 + r) for r

Answer 14

r = (A - p)/ p

Question 15

Solve: y = mx + b for m

Answer 15

m = (y - b)/x

Question 16

Solve: G = 2b(R - r) for r

Answer 16

r = R - G/2b

Question 17

Solve: A = P + Prt for t

Answer 17

t = (A - P)/Pr

Question 18

Solve: A = 0.5h(b + B) for h

Answer 18

h = (2A)/ b + B

Question 19

Solve: A = 0.5h(b + B) for b

Answer 19

b = (2A)/h - B

Question 20

Solve: A = 0.5hb + B for b

Answer 20

b = 2(A - B)/ h

Question 21

Solve: F = (9/5)C + 32 for C

Answer 21

C = 5/9(F - 32)

Question 22

Solve: C = 1 - A/b for A

Answer 22

A = b(1 - C)

Question 23

Solve: x/2 + y = z² for x

Answer 23

x = 2(z² - y)

Question 24

Solve: F = (GmM)/d² for m

Answer 24

m = (Fd²)/GM

Question 25

Solve: a² = b² + c² for b

Question 26

Find three consecutive odds such that three times the middle one is one more than the sum of the first and the third.

Answer 26

-1 1 and 3

Question 27

12) Twice the smallest of three consecutive even integers is 6 more than the largest one. Find the integers.

Question 28

Find the number such that 5 times three more than itself is 80.

Answer 28

13

Question 29

Four times the sum of twice a number and 23 is 76. Find the number.

Answer 29

-2

Question 30

A wallpaper hanger charges a fee of $25 plus $12 per roll of wallpaper. How many rolls were used if the total charge for hanging wallpaper is $97?

Answer 30

6

Question 31

A taxi charges $3.50 initially and $2.80 per kilometer. How many kilometers did a customer travel if his total taxi fare was $17.50?

Answer 31

5

Question 32

Solve A = P + Prt for P

Answer 32

(A)/ 1 + rt