Ratio problem forgot how to do it xD?

Question

Yeah, left my textbook at school..anway:
The ratio of boys to girls in a school is 2:3 IF there are 435 students in the school, how many boys and how many are girls?

To make standard concrete, gravel, sand and cement are mixed in the ratio of 5:3:1. I wish to make 27tonne of concrete. How much gravel sand and cement must I purchase?

Please include workin out so I figure the rest out for myself :)

Answer 1

To find the individual components when given the total number of individual units, simply add up all the parts of the ratio and divide into the total number of units to find the value of 1 unit. Then multiply each part of the ratio by the value of 1 unit:

2x (boys) + 3x (girls) = 435 students
5x = 435 students
x = 87 students
Therefore:

2(87) = 174 boys
3(87) = 261 girls

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5x (gravel) + 3x (sand) + 1x (cement) = 27 tonne concrete
9x = 27 tonne
x = 3 tonne
Therefore:

5(3) = 15 tonne gravel
3(3) = 9 tonne sand
1(3) = 3 tonne cement

Good luck with the rest.

Answer 2

The ratio 2 : 3 Means 2 boys and 3 girls a total of five (5)

435 Total students

The new ratio becomes 2 / 5 = boys and 3 / 5 = girls

Finding the amount of boys

435 (2/5) = 870/5 = 174 boys

Finding the amount of girls

437 (3/5) = 1305/5 - 261 Girls

The answer is: 174 boys and 261 girls

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5 : 3 : 1 = 9 Total tons

5/9 = Gravel

3/9 = Sand

1/9 = Cement

27 = Total tons of concrete

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Finding tons on gravel

27 (5/9) = 135/9 = 15 Tons gravel

Finding tons of sand

27(3/9) = 81/9 = 9 Tons of sand

Finding ton of cement

27 (1/9) = 27 = 3 Tons of cement

The answer is 15 tons of gravel, 9 tons of sand and 3 tons of cement.

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Answer 3

Think of the smallest group you could make with the boy:girl ratio 2:3. 2 boys and 3 girls. so of your 5 students 2 are boys and 3 are girls. So 2/5 of the students in your school are male and 3/5 are female.
Total number of boys = 435*(2/5)
Total number of girls = 435*(3/5)

With the concrete problem think of the smallest amount which could be made using no less than a tonne of each substance. 5:3:1 gives 5tonnes of gravel + 3 tonnes of sand + 1 tonnes of cement. this is 9 tonnes total with 5/9ths gravel, 3/9ths sand and 1/9th cement.

So for 27 tonnes of concrete you need

27*(5/9)tonnes of gravel
27*(3/9)tonnes of sand
27*(1/9)tonnes of cement

Answer 4

-->174 boys, 261 girls
2x + 3x =435
x=87
2(87)=174
3(87)=261

-->15 gravel, 9 sand and 3 cement.....