Mathematics, 22.06.2020 18:57, lelliott86

Students in a school are asked to pick either football, rugby or tennis to play in their lessons. the number of students who picked football and rugby are in the ratio of 4:3 the number of students who picked rugby and tennis in the ratio of 9:19 57 students picked tennis work out how many student picked football

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answered: marrizza7

36 Students picked football

Step-by-step explanation: When calculating values by the use of given ratios, it is important to note that the ratio of one value as compared to the other is the same as the actual value compared to the other.

The ratio of students who picked rugby and tennis is given as ratio 9 : 19, which means for every 28 students (that was derived by 9 + 19), 9 would choose rugby and 19 would choose tennis. However, we have been given the total number of students who chose tennis as 57, hence the value 57 would now replace the ratio of 19. However the total number of those who chose rugby is not yet known, so we can write out an equation as shown below;

19/28 = t/x

Where t is the number of tennis players as represented by ratio 19 and x is the total number of both tennis and rugby players as represented by 28.

By cross multiplication we now have

19 * x = 28 * 57

x = (28 * 57)/19

x = 1596/19

x = 84

If a total of 84 students play both rugby and tennis, and 57 of them play only tennis, then the number of rugby players is derived as

r = x - t

r = 84 - 57

r = 27

Having determined that 27 students played rugby, and the ratio of football to rugby players is given as 4 : 3, the relationship can be mathematically represented as follows;

3/7 = r/y

Where r is the total number of rugby players and y is the total number of both football and rugby players

3/7 = 27/y

By cross multiplication you now have

3 * y = 7 * 27

y = (7 * 27)/3

y = 189/3

y = 63

If the total number of football and rugby players is 63 and out of these 27 play rugby only, then the number of football players is derived as;

f = y - r

f = 63 - 27

f = 36

Therefore the number of students who chose football is 36

answered: Guest

the system of inequity is

$y\leq -x+4$

$3y> x$

step-by-step explanation:

from the given graph it is noticed that we have two related lines. one is solid and another is dashed.

if a line passing through two points, then the equation of line is

$y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$

the solid line passing through the points (0,4) and (4,0).

$y-4=\frac{0-4}{4-0}(x-0)$

$y=-x+4$

the related equation of solid line is $y=-x+4$ .

similarly, find the related equation of dashed line. the dashed liune passing through the points (0,0) and (3,1).

$y-0=\frac{0-1}{3-0}(x-0)$

$3y=x$

the related equation of dashed line is $3y=x$

from the given graph it is noticed that the point (0,1) lies on the shaded region, therefore the point (0,1) must be satisfied by the related equations.

check the related equations by the point (0,1).

$1=-0+4$

$1=4$

this statement is true if the sign of inequality is < instead of equality. since it is an solid line therefore the sign of inequality will be $\leq$ . the required inequality is