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
Answer:
----- 14
-----4 years (read my question)
----- 35
----- $20
Step-by-step 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
