Question

Amy had 3 times as much money as Betty. After they had spent $60 each, Amy had 4 times as much money as Betty. How much money did Amy have at first?

Answer 1

Answer:

Money with Amy initially is $540.

Step-by-step explanation:

Let the initial money with Amy and Betty be x and y.

★ According to the first condition, Amy had 3 times as much money as Betty.

$\longrightarrow$ x = 3y ---- (Equation I)

Money left after spending $60 :

• Amy = (x – 60)
• Betty = (y – 60)

★ According to the second condition,

After spending $60, Amy had 4 times as much money as Betty.

$\longrightarrow$ (x – 60) = 4(y – 60)

$\longrightarrow$ x – 60 = 4y – 240

$\longrightarrow$ 3y – 60 = 4y – 240 ----- (Substitute equation I)

$\longrightarrow$ 3y – 4y = –240 + 60

$\longrightarrow$ –y = –180

$\longrightarrow$ y = 180

Money with Betty = $180

________________________

★ Money with Amy :

Substitute the value of y in equation I.

$\longrightarrow$ x = 3(180)

$\longrightarrow$ x = 540

Money with Amy = $540

Therefore, money with Amy initially is $540.

Answer 2

Money with Amy initially is $540.

Step-by-step explanation:

Let the initial money with Amy and Betty be x and y.

★ According to the first condition, Amy had 3 times as much money as Betty.

⟶ x = 3y ---- (Equation I)

Money left after spending $60 :

Amy = (x – 60)

Betty = (y – 60)

★ According to the second condition,

After spending $60, Amy had 4 times as much money as Betty.

⟶ (x – 60) = 4(y – 60)

⟶ x – 60 = 4y – 240

⟶ 3y – 60 = 4y – 240 ----- (Substitute equation I)

⟶ 3y – 4y = –240 + 60

⟶ –y = –180

⟶ y = 180

Money with Betty = $180

________________________

★ Money with Amy :

Substitute the value of y in equation I.

⟶ x = 3(180)

⟶ x = 540

Money with Amy = $540

Therefore, money with Amy initially is $540.