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
is autonomous
is *not* autonomous