[formulaspart2][section10]

(1.) R = 3.50A + 1.50C use this formula

On Wednesday, total receipts at the Trylon Theater

amounted to $623 and 151 adult tickets were sold. How many

children's tickets were sold?

R = 3.50A + 1.50C use this formula

623 = 3.50(151) + 1.50C replace R and A with 623 & 151

623 = 528.50 + 1.50C multiply

-528.50 -528.50 subtract this from each side
________________________
94.5 = 1.50C subtract
_______ ______
1.50 1.50 divide each side by 1.50

63 = C divide and cancel

result: 63 children's tickets were sold.

(2.) R = 3.50A + 1.50C use this formula

For the Saturday matinee, the Trylon Theater sold 472

children's tickets. Total receipts were $1646. How many

adult tickets were sold?

R = 3.50A + 1.50C use this formula

1646 = 3.50A + 1.50(472) replace R & C with 1646 & 472

1646 = 3.50A + 708 multiply

-708 -708 subtract 708 from each side
_______________________
938 = 3.50A subtract
_____ ______
3.50 3.50 divide each side by 3.50

268 = A divide and cancel

result: 268 adult tickets were sold

(3.) The yearly interest, i, in dollars on an investment, p,

earning 14 1/2 % interest is given by the formula i = 0.145p .

What investment will earn 181.25 in interest in 1 year?

i = 0.145p use this formula

181.25 = 0.145p replace i with 181.25
_______ ______
0.145 0.145 divide each side by 0.145

p = $1250 divide and cancel

result: p = 1250

(4.) Use this formula: M = (1 - P)C

The mortgage, M, on a house is 60,000 and the percent of down

payment is 25 % . Find the cost of the house.

M = (1 - P)C use this formula

60,000 = (1 - .25)C replace M & P with 60,000 & .25

60,000 = .75C subtract
_______ _____
.75 .75 divide each side by .75

C = 80,000 divide and cancel

result: The cost of the house is $80,000 .

(5.) Use this formula: M = (1 - P)C

The mortgage, M, on a house is $45,000 and the percent of

down payment is 20 % . Find the cost of the house.

Use this formula: M = (1 - P)C

45,000 = (1 - .20)C replace M and P with 45,000 & .20

45,000 = .80C subtract
_______ _____
.80 .80 divide each side by .80

56,250 = C divide and cancel

result: The cost of the house is $56,250 .

(6.) Use this formula: d = rt

Find the time required for a jet to travel 45 km at a speed

of 900 km/hr.

Use this formula: d = rt

45 = 900t replace d with 45
____ ____
900 900 divide each side by 900

.05 = t divide and cancel

t = .05(60) multiply by 60 to change to minutes

t = 3 minutes multiply

result: 3 minutes

(7.) Use this formula: W = 265 + 0.03S

This week, the salesperson's wages were $460. Find the total

sales.

Use this formula: W = 265 + 0.03S

460 = 265 + 0.03S replace w with 460

-265 -265 subtract 265 from each side
______________________
195 = 0.03S subtract
____ _______
0.03 0.03 divide each side by 0.03

6500 = S divide and cancel

result: The total sales was $6500 .

(8.) Use this formula: W = 265 + 0.03S

What were the salesperson's total sales for a week in which the

total weekly wages were $403.30?

Use this formula: W = 265 + 0.03S

403.30 = 265 + 0.03S replace W with 403.30

-265 -265 subtract 265 from each side
_______________________
138.30 = 0.03S subtract
_______ _____
0.03 0.03 divide each side by 0.03

4610 = S divide and cancel

result: The total sales were $4610 .

(9.) Use this formula: S = 2(pi)rh + 2(pi)r²

[The surface area of a cylinder.

Find h given S = 105 and r = 3.

Use this formula: S = 2(pi)rh + 2(pi)r²

105 = 2(pi)(3)h + 2(pi)(3)² make substitutions

105 = 6(pi)h + 18(pi) multiply

-18pi -18pi subtract 18pi from each side
______________________
105 - 18pi = 6(pi)h subtract
____ ____ _______
6pi 6pi 6pi divide thru by 6pi

(17.5/pi) - 3 = h divide and cancel

result: h = (17.5/pi) - 3

(10.) Use this formula: A = P(1 + r)^t

Find P if A = 6083.26 and r = 4 % and t = 5.

6083.26 = P(1 + .04)⁵ make substitutions

6083.26 = P(1.04)⁵ add

6083.26 = 1.2166529024P raise 1.04 to the 5th power
________ ________________
1.2166529024 1.2166529024 divide each side by 1.2166529024

5000 = P divide and cancel

result: P = 5000