Question

Drag the tiles to the correct boxes to complete the pairs. Match each word problem to its solution. Seven more than 3 times a number is 49. What is the number? Hillary's age is 3 years greater than times Lily's age. If Hillary is 19 years old, how old is Lily? Twice a number decreased by 20 is 50. What is the number? Claret purchased two handbags and a wallet. The cost of each handbag was $10 more than the wallet. If she spent a total of $60 for the two handbags, what is the cost of the wallet? 35 arrowBoth 20 arrowBoth 14 arrowBoth 24 arrowBoth

Answer 1

----- 14

-----4 years (read my question)

----- 35

----- $20

Explanation:

We will derive the answers statement by statement.

------Seven more than 3 times a number is 49

Let's assume the number to be x

3x + 7 = 49

3x = 42

X = 14

------Hillary's age is 3 years greater than 4 times Lily's age. If Hillary is 19 years old, how old is Lily?

Let Lily's age be x

4x + 3 = 19

4x = 16

X = 4

Lily's is 4 years old

-----Twice a number decreased by 20 is 50.What is the number?

Let's assume the number to be x

2x - 20 = 50

2x = 70

X = 35

------Claret purchased two handbags and a wallet. The cost of each handbag was $10 more than the wallet. If she spent a total of $60 for the two handbags, what is the cost of the wallet?

Let the cost of the wallet be x

Since the cost of each handbag is $10 more than the cost of the wallet,the cost if handbag is then

X + 10

If she spent $60 for the 2 handbags,

2(x + 10) = 60

2x + 20 = 60

2x = 40

X = $20

The cost of the wallet is $20

Answer 2

Answer: (A) The number is 14

(B) Lily is 16 years old

(C)The number is 35

(D) The wallet cost $20

Step-by-step explanation: (A) Let the number be a. Three times the number is equal to 3 times a, or 3a. Seven more than 3a equals 49, that means

7 + 3a = 49

Subtract 7 from both sides of the equation

3a = 42

Divide both sides of the equation by 3

a = 14

The number is 14

(B) Let Hillary's age be h and Lily's age be l, so if Hillary's age is 3 years greater than Lily's age, then we have

h = 3 + l

Then if Hillary's age is now given as 19, the equation becomes

19 = 3 + l

Subtract 3 from both sides of the equation

16 = l

Lily's age is 16

(C) Let the number be x, and so twice the number becomes 2 times x which is 2x. Twice the number decreased by 20 is 50, becomes

2x - 20 = 50

Add 20 to both sides of the equation

2x = 70

Divide both sides of the equation by 2

x = 35

The number is 35

(D) Let each handbag be represented by b and each wallet be represented by w. The cost of each handbag is 10 more than the wallet, so if the wallet cost w, then the handbag would cost w + 10. This can be expressed as

h = w + 10

If she spent a total of 60 for the 2 handbags, then each handbag would cost 60 ÷ 2 which equals 30 per handbag. Substituting for the known value we now have,

30 = w + 10

Subtract 10 from both sides of the equation

20 = w

The cost of a wallet is $20