A fruiterer has some apples and pears in the ratio of 2:5. He sold 261 pears and bought 261 more apples. After that, he had as many apples and pears. How many apples did he have at first.

The number of apples the fruitier have at first is 348 apples

Step-by-step explanation:

The given parameters are;

The ration of the apples to pears the fruitier has = 2:5

The number of pears he sold = 261 pears

The number of apples he bought = 261 apples

The new ratio of apples to pears the fruitier then has =  1:1

Let 'x', represent the initial number of apples the fruitier has at first, and let 'y', represent the initial number of pears the fruitier has at first

Therefore, we have; x:y = 2:5

x/y = 2/5

∴ 5·x = 2·y

x = 2·y/5...(1)

(x + 261):(y - 261) = 1:1

∴ (x + 261)/(y - 261) = 1

x + 261 = y - 261...(2)

Substituting the value of 'x' from equation (1) in equation (2), gives;

2·y/5 + 261 = y - 261

261 + 261 = y - 2·y/5 = 3·y/5

522 = 3·y/5

∴ y = 5 × 522/3 = 870

The number of pears the fruitier have at first, y = 870 pears

x = 2·y/5 = 2 × 870/5 = 348

The number of apples the fruitier have at first, x = 348 apples.

question 1 is 8, question 2 is 9, question 3 is 24

step-by-step explanation:

now, the numbers they give you at the top are the key. from there, you just have to plug and chug! let's try 1, 2, and 3!

key: a=3, b=5, c=6

1. a+5

remember, a=3, so we plug that in to get 3+5=8

2. 15-c

c=6, so we plug that in to get 15-6=9

3. 4b

b=6, so we plug it in to get 4*6=24

time to try the rest on your own! if you put the answers below in a comment, i'll check them for you!

answer is 8x+24

area of vanessa's patio = length × width

given, length = (3x² + 5x + 10)

width = (x² - 3x - 1)

area of vanessa's patio = (3x² + 5x + 10)(x² - 3x - 1)

= 3x²(x² - 3x - 1) + 5x(x² - 3x - 1) + 10(x² - 3x - 1)

= 3x⁴ - 9x³ - 3x² + 5x³ - 15x² - 5x + 10x² - 30x - 10

= 3x⁴ - 4x³ - 8x² - 35x - 10

hence, expression of vanessa's patio = (3x⁴ - 4x³ - 8x² - 35x - 10)