Topic: forming and solving equations (an equation must be included as well )

include all working out!

1)tom and ellie both have the same amount of money to begin with. tom multiplies his by 4 and adds up 50p. ellie multiplies hers by 9 and subtracts £3. they end up with the same amount of money. calculate the amount of money they started with.

2) alex thinks of a number. he adds 18 then divides it by 2. he gets the same answer that he would have if he had multiplies the original number by 5. calculate the mystery number.

Question 1= 70p; Question 2=2

Step-by-step explanation:

Question 1) Since Tom and Ellie have equal amount, let the amount be X (in Penny)

Tom multiplied his amount by 4= 4X, he then adds 50p = 4X + 50

Ellie multiplied hers by 9= 9X, she then subtracts €3, since we are working with Penny, we have to convert €3 to Penny, which is 300p. We have 9X - 300

Since the resulting amounts of Tom and Ellie are equal, we can say

4X + 50 = 9X - 300

We then collect like terms by moving like terms in opposite direction of the equation to have,

9X - 4X = 300 + 50

5X = 350

We divide both sides by the coefficient of X, which is 5

X = 70

Hence, the amount Tom and Ellie started with is 70p.

Question 2) Let the number Alex thinks of be X

He adds 18 = X + 18

He divides the result by 2= X + 18 / 2

Since he would have gotten the same answer if he multiplied X by 5, which is 5X

We can say, X+18/2 = 5X

We then cross multiply, 2 cross multiplies 5X to give 10X while 1 cross multiplies X + 18 to give X+18

We then have, X+18=10X

We collect like terms by moving X to the opposite side of the equation

We then have 18=10X-X

18=9X

Divide both sides by the coefficient of X, which is 9

X=2

Therefore, the number Alex thinks of is 2