Some students planned for a picnic. The budget for the food was 480dollars. As 8 of them failed to join the party, the cost of food for each member increased by 10 dollars .Find how many students went for the picnic

16 students went for the party

Step-by-step explanation: First of all, let us represent the number of students that went for the party by x. The budget for the food was 480, that means each person was supposed to pay 480/x.Next we shall represent the cost per student by letter y, that means

480/x = y (1)

However, 8 of them failed to show up and so the cost per person increased by 10. This can be expressed as follows;

480/(x - 8) = y + 10 (2)

From equation (2) note that the number of students x, has reduced by 8. and then the cost per student y, has increased by 10.

We shall now solve for the pair of simultaneous equations

480/x = y (1)

480/(x - 8) = y + 10 (2)

Substitute for y = 480/x into equation (2)

480/(x - 8) = 480/x + 10

480/(x - 8) = (480 +10x)/x

By cross multiplication we now have,

480x = (480 + 10x) (x - 8)

480x = 480x - 3840 + 10x² - 80x

Collecting like terms we now have;

10x² - 80x -3840 = 0

Divide all through by 10

x² - 8x - 384 = 0

We now solve for the quadratic equation by factorization

(x + 16) (x - 24) = 0

(x + 16) = 0      OR

(x - 24) = 0

Therefore, x = -16     OR

x = 24

Knowing that we cant have a negative value, we shall take x = 24.

So, having determined that 24 students planned for the picnic, and 8 of them failed to join the party, then it turns out that only 16 students went for the picnic (that is, 24 - 8).

3. parallelogram

step-by-step explanation:

we turn each of our sides into direction vectors

ab=b-a=(3 - 7, 1 - 0) = (-4, 1)

bc=c-b=(1,6)

cd=d-c=(4,-1)

da=a-d=(-1,-6)

we see how the opposite sides have negated direction vectors; this is characteristic of a parallelogram.   we have congruent sides ab=cd and bc=da with unequal lengths because 1^2+6^2 is different from (-4)^2+1^2.   so it's not a square or a rhombus.  

we check the dot product of direction vectors of adjacent sides.   we have

ab dot bc = -4(1) + 1(6) = 2

that's not zero so the sides are not perpendicular.   we've ruled out rectangle.

the direction vectors indicate two pairs of congruent parallel sides, so we choose parallelogram over trapezoid.

37/3

step-by-step explanation:

step 1: simplify both sides of the equation.

7x+8(x+

1

4

)=3(6x−9)−8

7x+(8)(x)+(8)(

1

4

)=(3)(6x)+(3)(−9)+−8(distribute)

7x+8x+2=18x+−27+−8

(7x+8x)+(2)=(18x)+(−27+−8)(combine like terms)

15x+2=18x+−35

15x+2=18x−35

tep 2: subtract 18x from both sides.

15x+2−18x=18x−35−18x

−3x+2=−35

step 3: subtract 2 from both sides.

−3x+2−2=−35−2

−3x=−37

step 4: divide both sides by -3.

−3x

−3

=

−37

−3

x=

37

3