Ratios

[Ams627]

During swimming training, Jirka, Míša and Pavla swam a total of 126 lengths. Míša swam a third more lengths than Jirka and twice as many lengths as Pavla. Calculate how many lengths Míša swam in training.

M = 4J / 3 M = 2P

J + M + P = 126

3M/4 + M + M/2 = 126

[Ams627]

At the nut store, they mix a mixture of peanuts and almonds and sell it in different sized packages. One hundred grams of this mixture is sold for 20 crowns, while one hundred grams of peanuts costs 10 crowns. Tereza bought an 800 gram package of this mixture. There are always 300 g of peanuts in such a package. The price of the mixture depends only on the weight and price of the raw materials used.

How much do one hundred grams of almonds cost?

[Ams627]

[From homework - can be reused] A wheelbarrow can carry half as much weight as a small trolley. There can be four times more weight on a big trolley than a small trolley. All three vehicles can transport 770kg at the same time. How much can be transported on a small trolley.

ratios are 0.5 : 1 : 4 In other words x + 2x + 8x = 770, so 11x = 770, x = 70.

Without "equations" The way to see this is that it is the same as 11 small trolleys.

[Ams627]

There are 24 students in the class. Each student chose one of three foreign languages: English, German, or Spanish. Every fourth pupil chose German. Twice as many pupils chose English as Spanish.

Determine the number of students who chose English.

Express in basic form the progressive ratio of the number of students who chose individual languages, namely English, German, Spanish.

Solution: Every fourth pupil chose German, so that's 6 choosing German and 18 remaining. The 18 remaining are in the ratio 2:1, so we divide 18 by 3 and then multiply by 2 to get English.

So English is 12 and Spanish 6. Ratio is 2:1:1.