A certain restaurant offers 6 kinds of cheese and 2 kinds of fruit for its dessert platter. If each dessert platter contains an equal number of kinds of cheese and kinds of fruit, how many different dessert platters could the restaurant offer?

Solution:

Given that,

A certain restaurant offers 6 kinds of cheese and 2 kinds of fruit for its dessert platter

Each dessert platter contains an equal number of kinds of cheese and kinds of fruit

For this problem there are two scenarios:

1 ) one cheese and one fruit

2 ) two cheese and two fruit

For one cheese and one fruit

Use the combination formula

Where, n is total items and r is the items being chosen at a time

For 2 cheese and 2 fruits

So, total ways = 12 + 15 = 27

Thus, 27 different dessert platters can be offered by restaurant

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

answer: x=60