Question

Please Help! Not good with word problems! THANK YOU

Answer 1

QUESTION 1

Let the number be
`x`.

If this number is decreased by 32 and the result is -58, then we can write the following equation and solve for
`x`.

`x-32=-58`.

Group the similar terms to get;

`x=-58+32`

`x=-26`

The number is -26.

QUESTION 2

The product of 14 and
`n` is
`14* n=14n`

If the product is -28, then the require algebraic equation is

`14n=-28`

QUESTION 3

Let the number be
`y`.

Four times this number is
`4y`.

The number increased by 78 is
`y+78`.

If four times the number is the same as the number increased by 78, then we write and solve the equation;

`4y=y+78`

Group the similar terms;

`4y-y=78`

Simplify

`3y=78`

Divide both sides by 3;

`y=(78)/(3)`

`y=26`

The number is 26

QUESTION 4

Let
`b` represent the price of the blue bike and
`r` represent the price of the red bike.

Then we can write the following two equations and solve simultaneously.

`b=r-14...(1)`

`b+r=300...(2)`

We substitute equation (1) into equation (2) to obtain;

`r-14+r=300`

Group like terms;

`r+r=300+14`

Simplify;

`2r=314`

Divide both sides by 2

`r=157`

The red bike is $157

and

The blue bike is 157-14=$143

QUESTION 5

Let
`a` represent the age of Alex and
`e` represent the age of his sister. Then;

`a=e+6...(1)`

`a+e=32..(2)`

Put equation (1) into equation (2) to get;

`e+6+e=32`

`\Rightarrow e+e=32-6`

`\Rightarrow 2e=26`

`\Rightarrow e=13`

Alex is 13+6=19 years old.

QUESTION 6

Let
`c` represent Mrs computer's age and
`m` represent Mousy's age. Then;

`c=3m...(1)`

`c+m=52...(2)`

Put equation (1) into equation (2).

`\Rightarrow 3m+m=52`

`\Rightarrow 4m=52`

`\Rightarrow m=(52)/(4)`

`\Rightarrow m=13`

Mousy is 13 years old.

QUESTION 7.

Let Mike be
`m` years and Tom be
`t` years.

Then;

`m=2t+5...(1)`

`m+t=65...(2)`

Put equation (1) into equation (2) and solve.

`\Rightarrow 2t+5+t=65`

`\Rightarrow 2t+t=65-5`

`\Rightarrow 3t=60`

`\Rightarrow t=(60)/(3)`

`\Rightarrow t=20`

Mike is 2(20)+5=45 years old.

QUESTION 8

Let the consecutive integers be

`x,x+1,x+2`

The sum of the second and third is 17 gives the equation;

`(x+1)+(x+2)=17`

The second choice is correct

QUESTION 9

Let the consecutive integers be

`x,x+1,x+2`

Their sum being 108 gives the equation

`x+x+1+x+2=108`

Regroup

`x+x+x+1+2=108`

Simplify the LHS

`3x+3=108`

Factor the LHS

`3(x+1)=108`

Correct choice is A

QUESTION 10

Let the two consecutive odd integers be;

`x,x+2`

The sum being 72 gives the equation;

`x+x+2=72`

Simplify the first two terms

`2x+2=72`

Answer 2

Ques 1)

A number decreased by 32 is -58.

Let the number be 'x'.

i.e. x-32=-58

⇒ x= -58+32

⇒ x= -26.

Hence the number is -26.

Ques 2)

The product of 14 and n is -28.

The expression is:

⇒ 14n= -28

on solving we get:

n= -2 ( since on dividing both side by 14)

Ques 3)

Let the number be 'x'.

i.e. 4x=x+78

4x-x=78

3x=78

x=26.

Hence, the number is 26.

Ques 4)

Let the price of red bike is $ r.

so, the cost of blue bike is: $ (r-14)

also, r+r-14=300

2r-14=300

2r=314

r=157

Hence, the cost of red bike is: 157

and the cost of blue bike is: 143

Ques 5)

Let the age of Emma is: x years.

and the age of Alex is x+6 years.

Also,

x+x+6=32

2x+6=32

2x=32-6

2x=22

x=11.

Hence, age of Emma is 11 years.

and age of Alex is 17 years.

Ques 6)

Let age of Mousy is x years.

and age of Mrs. computer= 3x years.

Also,

x+3x=52

4x=52

x=13

Hence age of Mousy is 13 years.

and age of Mrs. Computer is 39 years.

Ques 7)

Let the age of Tom is x years.

so, the age of Mike is (2x+5) years.

Hence,

2x+5+x=65

3x+5=65

3x=60

x=20.

Hence, age of Tom is 20 years.

and age of Mike is: 2×20+5=45 years.

Ques 8)

Let the first integer is 'x'.

second integer is (x+1)

third integer is: (x+2)

Hence, the expression is given as:

(x+1)+(x+2)=17

Ques 9)

Let the first integer is 'x'.

second integer is (x+1)

third integer is: (x+2)

There sum is 108.

Hence,

x+x+1+x+2=108

3x+3=108

Ques 10)

Let the first odd integer is x

the next odd integer will be: x+2.

There sum is 72.

Hence,

x+x+2=72

i.e. 2x+2=72