Question

1. Sam solved the following problem:

-4x + 5 > 29
-4x + 5 - 5 > 29 - 5
-4x > -24
-4x/-4 > -24/-4
x > 6

What were his two mistakes? (3 points)


2. Hillary buys 3 pounds of Gala apples and some Granny Smith apples. Both kinds of apples cost $4.50 per pound. The total cost is $24.75. How many pounds of Granny Smith apples did Hillary buy? Write and solve a variable equation. Show your work.
(4 points)



3. Tell whether each equation has one solution, infinitely many solutions, or no solution. (3 points)

6x + 8 = 6(x + 2)
10x = 15 + 5x
x + 11 = 8x + 11 - 7x

Answer 1

(A) From above five steps , it is found that Sam made mistake at step ( I I I ) and step (I V) .

(B) The quantity of Granny smith apples bought is 2.5 pounds .

(C) (i) The equation has No solution

(ii) The equation has one solution

(iii) The equation has infinite many solution .

Explanation:

Given as :

(A) The inequality expression

( I ) -4 x + 5 > 29

( I I ) -4 x + 5 - 5 > 29 - 5 (Add - 5 both side )

( I I I ) -4 x + 0 > 24

(I V )
`( - 4 x)/( -4)` >
`( 24)/( - 4)` (Dividing both side by - 4 )

( V ) x > - 6

Hence, From above five steps , it is found that Sam made mistake at step ( I I I ) and step (I V) . Answer

(B) Given as :

The quantity of Gala apples bought = 3 pounds

Let The quantity of Granny smith apples bought = x pounds

The cost of Gala apples = $4.50 per pound

The cost of Granny smith apples = $4.50 per pound

The total cost of the both apples = $24.75

Now, According to question

The total cost of the both apples = quantity of Gala apples bought × cost of Gala apples + quantity of Granny smith apples bought × cost of Granny smith apples

i.e 3 pound × $4.50 per pound + x pound × $4.50 per pound = $24.75

Or, $13.5 + x pound × $4.50 per pound = $24.75

Or, x pound × $4.50 per pound = $24.75 - $13.5

Or, x pound × $4.50 per pound = $11.25

Or, 4.50 x = 11.25

∴ x =
`(11.25)/(4.50)`

i.e x = 2.5

So, The quantity of Granny smith apples bought = x = 2.5 pounds

Hence,The quantity of Granny smith apples bought is 2.5 pounds . Answer

(C) Given as

The linear equations are

(i) 6 x + 8 = 6 × (x + 2)

Rearranging the equation

6 x + 8 = 6 x + 12

Or, (6 x - 6 x) = 12 - 8

Or, 0 = 4

So, The equation has no-solution

(ii) 10 x = 15 + 5 x

Or, 10 x - 5 x = 15

Or, 5 x = 15

∴ x =
`(15)/(5)`

i.e x = 3

So, The equation has one solution

(iii) x + 11 = 8 x + 11 - 7 x

Rearranging the equation

x + 11 = (8 x - 7 x) + 11

Or, x + 11 = x + 11

Or, x - x = 11 - 11

i.e 0 = 0

So, The equation has infinite many solution

Hence, (i) The equation has No solution

(ii) The equation has one solution

(iii) The equation has infinite many solution . Answer