Dividing in a Ratio

A communications specialist is preparing a field antenna and needs to cut a $60$-foot spool of copper wire into two sections in a ratio of $7:3$.

A flight line supervisor is dividing $480$ hours of scheduled maintenance tasks between two mechanic crews in a ratio of $3:5$. If the larger share of hours is assigned to the senior crew, how many maintenance hours does the senior crew receive?

A base commander is distributing a total of $240$ new combat helmets to two platoons in a ratio of $5:3$. How many helmets will the platoon with the smaller share receive?

A naval base allocates its quarterly maintenance budget among structural repairs, mechanical overhauls, and routine inspections in the ratio of $5:8:2$. The amount allocated for mechanical overhauls is $\$45,000$ more than the amount allocated for routine inspections. Based on this information, calculate the total quarterly maintenance budget.

An aviation maintenance team is preparing a specialized anti-icing fluid blend consisting of glycol, water, and an additive in the ratio of $8:3:1$ by volume. If the team needs to prepare a total of $60$ gallons of this fluid, how many more quarts of glycol are required than water?

A motor pool technician is mixing a cleaning solvent and water in a ratio of $2:5$ to fill a $35$-gallon container. How many gallons of cleaning solvent are needed?

A supply sergeant initially distributes $2,400$ rounds of specialized training ammunition among three firing squads—Alpha, Bravo, and Charlie—in a ratio of $2:3:5$, respectively. During the drill, Squad Bravo requests and is issued exactly $180$ additional rounds.

To maintain the exact original $2:3:5$ distribution ratio among the three squads, the sergeant must also issue additional rounds to Alpha and Charlie. How many total additional rounds must be issued to Squads Alpha and Charlie combined to perfectly restore the original ratio?

A mess hall cook prepares a large batch of stew. The recipe requires a total of $60$ pounds of meat and potatoes. If the ratio of meat to potatoes is $3:2$, how many pounds of meat are needed?

A logistics officer needs to distribute $150$ tactical backpacks between two infantry squads in a ratio of $2:3$. How many backpacks will the squad with the smaller share receive?

During a base renovation, a carpenter cuts a $5$-foot wooden board into two pieces. If the lengths of the two pieces are in a ratio of $2:3$, what is the length of the shorter piece in inches?

A combat engineering detachment is mixing a specialized rapid-setting concrete. The dry mix requires sand, gravel, and cement in a ratio of $4:5:2$ by weight. If the engineers need to prepare exactly $3,300$ pounds of the dry mix for a runway repair, how many pounds of gravel are required?

A refueling truck contains $150$ gallons of aviation fuel. The fuel is distributed among three training aircraft in a ratio of $2:3:5$. How many quarts of fuel does the second aircraft receive? ($1\text{ gallon} = 4\text{ quarts}$)

Read the scenario and fill in the missing values based on the given ratio.

A construction crew is pouring a foundation that requires $3.6$ tons of a custom gravel and sand mixture. If the mixture contains gravel and sand in a ratio of $5:4$, how many pounds of sand are required for the foundation? ($1$ ton $= 2,000$ pounds)

A quartermaster is allocating $2,100$ yards of heavy-duty canvas to manufacture temporary shelters, cot covers, and equipment tarps. The canvas is divided among these three projects in a ratio of $6:5:3$, respectively. What is the difference, in yards, between the amount of canvas allocated for the temporary shelters and the amount allocated for the equipment tarps?

A supply sergeant is distributing $560$ pairs of cold-weather boots between two infantry companies (Company Alpha and Company Bravo) in a ratio of $3:4$. How many MORE pairs of boots does Company Bravo receive than Company Alpha?

A naval supply officer is allocating a $\$4,500$ monthly discretionary budget among three ship departments—Deck, Engineering, and Operations—in a ratio of $4:5:6$, respectively. Calculate the specific funding amounts based on this ratio.

A signal corps detachment has a continuous spool of tactical fiber optic cable that is $240$ meters long. A technician must cut the entire spool into three separate sections to establish command, perimeter, and relay links in a ratio of $2:3:5$ respectively. What is the length of the shortest section in centimeters?

A communications platoon is distributing a shipment of $8,400$ replacement radio batteries among three forward operating bases (FOB Alpha, FOB Bravo, and FOB Charlie) in a ratio of $4:5:6$, respectively. Based on this ratio, how many batteries will FOB Charlie receive?

A military supply depot distributes a shipment of Meals Ready-to-Eat (MREs) among three battalions: Alpha, Bravo, and Charlie. Battalion Alpha receives $\frac{1}{3}$ of the total shipment. The remaining MREs are then divided between Battalion Bravo and Battalion Charlie in a ratio of $3 : 5$ respectively. If Battalion Charlie receives exactly $1,200$ more MREs than Battalion Bravo, what is the total number of MREs in the entire shipment?