Mixture Problems: Difficult Problems with Solutions

Some alcohol solution is mixed with [tex]24[/tex] gallons of [tex]65\%[/tex] alcohol to get [tex]60[/tex] gallons of [tex]59\%[/tex] alcohol. What is the concentration of alcohol in the first solution (in %)?

Brass is an alloy of copper and zinc in which the weights of copper and zinc are in the ratio [tex]3:2[/tex]. How many pounds of zinc must be melted together with a brass block weighing [tex]4.4[/tex] lb to get a new alloy containing [tex]60\%[/tex] zinc?

A jeweler has [tex]1.4[/tex] ounces of pure gold. How many ounces of copper must be added to it to get [tex]14[/tex]-karat gold? (Pure gold is [tex]24[/tex]-karat.)

An alloy of copper and gold contains [tex]60\%[/tex] copper. After [tex]100[/tex] ounces of gold were added, the copper content dropped to [tex]40\%[/tex]. How many ounces of copper and how many ounces of gold does the new alloy contain?

A [tex]10[/tex]-gallon container is full of a [tex]40\%[/tex] acid solution. How many gallons must be poured out so that, after refilling the container with a [tex]30\%[/tex] solution of the same acid, the result is a [tex]37\%[/tex] solution?

A warehouse holds [tex]100[/tex] tons of cucumbers that are [tex]98\%[/tex] water. After some time the water content dropped to [tex]96\%[/tex]. How many tons of water evaporated?

Freshly threshed wheat usually has a moisture content of [tex]16\%[/tex]. After some drying, [tex]200[/tex] lb of grain became [tex]20[/tex] lb lighter. What is the moisture content of the grain after drying?

A [tex]10[/tex]-gallon container is full of a [tex]70\%[/tex] acid solution. Twice, [tex]1[/tex] gallon of liquid was poured out and the container was refilled with water. What is the concentration of the acid after the second refill?

An alloy of copper, zinc, lead and iron contains [tex]60\%[/tex] copper; the zinc is [tex]58\frac{1}{3}\%[/tex] of the copper, and the lead and the iron are in the ratio [tex]2:3[/tex]. How many pounds of copper, zinc, lead and iron (in this order) does the alloy contain if there is [tex]3.3[/tex] lb more zinc than lead?

A jeweler mixed three gold–copper alloys containing [tex]50\%[/tex], [tex]40\%[/tex] and [tex]30\%[/tex] gold. He took [tex]100[/tex] oz more of the second alloy than of the first, and twice as much of the third as of the first. How many ounces of each alloy must be taken so that the new alloy contains [tex]340[/tex] oz of pure gold?

One alloy contains gold and copper in the ratio [tex]2:3[/tex], and another in the ratio [tex]3:7[/tex]. How many ounces of each alloy must be taken to get [tex]120[/tex] oz of a new alloy in which gold and copper are in the ratio [tex]3:5[/tex]?

The octane number of gasoline equals the percentage of isooctane in it. A gas station owner topped up a partly filled tank of [tex]93[/tex]-octane gasoline with [tex]87[/tex]-octane gasoline. The full tank turned out to contain [tex]89[/tex]-octane gasoline, but he sold all of it at the price of [tex]93[/tex]-octane gasoline. The tank holds [tex]9000[/tex] gallons, and [tex]93[/tex]-octane gasoline costs [tex]30[/tex] cents per gallon more than [tex]87[/tex]-octane. How much extra profit did the dishonest dealer make?

One container holds a mixture of [tex]12[/tex] quarts of alcohol and [tex]20[/tex] quarts of water, and another holds [tex]9[/tex] quarts of alcohol and [tex]4[/tex] quarts of water. How many quarts must be poured from the first container into the second so that the second contains equal amounts of alcohol and water?

Melchior is an alloy of copper and nickel in the ratio [tex]4:1[/tex]. A workshop has [tex]6[/tex] lb of an alloy with copper and nickel in the ratio [tex]1:3[/tex] and [tex]8[/tex] lb of an alloy with copper and nickel in the ratio [tex]2:3[/tex]. How many pounds of pure copper must be added to the two alloys to get melchior?

Two containers hold acid solutions of unknown concentrations. Equal amounts from the two containers mixed together give a [tex]55\%[/tex] solution, and [tex]3[/tex] parts from the first container mixed with [tex]2[/tex] parts from the second give a [tex]51\%[/tex] solution. Find the concentration of the solution in each container.