Terence spent 20% of his savings on a watch and 30% of the remainder on a wallet. He had $840 left. What was the amount of money Terence had at first?

Answer 1

S - (20% times S) - (30% times .8S) = 840

S - .2S - .3(.8S) = 840

S - .44S = 840

.56S = 840

S = 840/.56 = 1500

20% = 1/5

1/5 of 1500 = 300

1500-300 = 1200

.3(1200) = 360

1200-360 = 840

He had $1500 to start

Answer 2

Terence spent 20% of his savings on a watch and 30% of the remainder on a wallet. He had $840 left. What was the amount of money Terence had at first?

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The key to word problems is converting the words into math equations. Each sentence is giving a hint to write the math equations. So......We use variables to represent unknown quantities and then we solve for the variables.

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Let S represent the Original Savings amount.

Let W represent the amount spent on watch.

Let M represent the amount spent on wallet.

......The question is asking for the value of S or how much he had at first. Before spending anything....

.....Each equation below represents a FACT taken from the word problem.....

20% x S = W...........20% of savings on a watch....

(S-W) x 30% = M........Remember you have subtract Wallet amount from the total for the "remainder"....

S-(W+M) = 840..........Every fact from the word problem is expressed as a math equation...840 left after

......after buying watch and wallet.

We now have 3 equations and 3 unknowns......a classic System of equations with various techniques of

......for solving.

.2S = W

.3S-.3W = M

S-(W+M) = 840

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.3S - .3 (.2S) = M

.3S - .06S=M

.24S = M....and..the first equation .2S = W

Substitute both of these equations into the third equation to isolate to 1 unknown variable S....

S - (.2S + .24S) = 840

S - .44S = 840

.56S = 840

S = 840/.56 = $1500.....so the original savings amount is S=$1500.....check your work...

M = .24 S = .24 (1500) = 360......and W = .2S = .2 (1500) = 300

..check 3rd equation...

S-(W+M) = 840 = 1500 - (360 + 300) = 1500 - 660 = 840....that checks out....

S = $1500....Original Savings

W = $300......Watch

M = $360......Wallet..