School Roof Solar Project

Solve multistep problems and use estimates to check results.

Project Records

Use the school solar project's records to solve each problem. Show your calculations. A negative balance means money is owed.

The project account has the following transactions.

Project Account
Entry	Amount
Starting balance	−$48.50
Five donations	$16.75 each
Supply purchase	$22.25 spent

What is the signed balance after all five donations and the purchase? $

During a seven-day test, the panels generate 18.5 kilowatt-hours (kWh) each day for four days and 9.75 kWh each day for three days. The school uses 100 kWh of that energy.

How much of the generated energy remains unused? kWh

An installer has a mounting rail that is 12 1/2 feet long. The installer cuts three pieces, each 2 3/4 feet long. Ignore material lost during cutting.

How much rail remains? Write a fraction or mixed number. feet

The project earns $19.60 in electricity credits each month for six months, then pays a $31.40 inspection fee. Round each dollar amount to the nearest ten dollars. Which calculation estimates the money left?

A. 6 × $20 + $30 = $150B. 6 × ($20 − $30) = −$60C. 6 × $20 − $30 = $90D. $20 − $30 = −$10

For this energy log, energy sent to the school is recorded as negative, and energy added to storage is positive. Storage starts at 0 kWh. The system sends 6 kWh to the school each hour for three hours, then adds 25 kWh to storage.

What is the signed net change in stored energy? kWh

Installation Decisions

Identify the operations needed before calculating. Keep units with your work.

The installation crew has 28.5 meters of cable. Two roof connections each use 8.75 meters, and a connection to the monitoring screen uses 4.6 meters.

How much cable remains after all three connections? meters

The project's account starts at −$12.50. It receives four electricity credits of $3.25 each, then pays a $2 monitoring fee. What is the final signed balance?

A. The final balance is −$11.25.B. The final balance is $23.50.C. The final balance is $2.50.D. The final balance is −$1.50.

The crew has a $90 budget for eight cable clips costing $7.50 each and one $18 shipping charge. How much of the budget will remain?

A. The crew will have $12 left.B. The crew will have $78 left.C. The crew will have $4.50 left.D. The crew will have $30 left.

A rail's position is measured relative to a marked line. Negative positions are below the line. The rail starts at −1 1/4 inches. A worker raises it by 3/8 inch three times, then lowers it by 1/2 inch.

What is the rail's final signed position? Write a fraction or mixed number. inch

10.

A battery begins a test with 3.6 kWh of stored energy. The school's monitoring equipment uses 0.75 kWh each hour for four hours. The panels then add 1.2 kWh to the battery.

How much energy is in the battery at the end of the test? kWh

Check the Results

Use the stated rounding method for each estimate. Keep estimates separate from exact answers.

11.

Over five days, the panels generate 14.8 kWh per day. During four of those days, a roof test uses 9.7 kWh per day; it uses no energy on the fifth day. Maya says 35.2 kWh remains. Round each daily energy amount to the nearest whole kWh. Which estimate supports her result?

A. About 115 kWh remains because 5 × 15 + 4 × 10 = 115.B. About 35 kWh remains because 5 × 15 − 4 × 10 = 35.C. About 25 kWh remains because 5 × (15 − 10) = 25.D. About 65 kWh remains because 5 × 15 − 10 = 65.

12.

The project has $82.40 available. It buys six warning labels for $7.85 each and pays one $12.30 delivery charge. First estimate the money left by rounding each dollar amount to the nearest whole dollar. Do not round the number of labels. Then find the exact amount left.

Estimated amount left: $
Exact amount left: $

13.

The solar project has $50 to buy three sensors at $12.95 each and one cable for $9.40. Luis rounds to whole dollars and estimates 3 × $13 + $9 = $48, so he says the budget is enough. Find the exact cost and the exact amount left. Explain why an estimate this close to the budget needs an exact check.