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 $14\times n=14n$

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;

$y=\frac{78}{3}$

$y=26$

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).

$\Rightarrow 3m+m=52$

$\Rightarrow 4m=52$

$\Rightarrow m=\frac{52}{4}$

$\Rightarrow m=13$

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.

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

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

$\Rightarrow 3t=60$

$\Rightarrow t=\frac{60}{3}$

$\Rightarrow t=20$

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

Answer:

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