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Money Word Problems

Money word problems are story problems that relate money and the objective of it to find out the amount or the number of coins given in the problem. To find out the unknown given in the word problem we apply the four arithmetic operations – addition, subtraction, multiplication and division. Few word problems require multi steps to solve where more than one arithmetic operation is applied. There are few money word problems that involves fraction too

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Examples

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Example 1: 

Cynthia goes to the mall for Christmas shopping. She buys cake worth $\$ 150$, Christmas tree worth $\$ 275$, chocolates worth $\$ 78$ and bouquet of flowers worth $\$ 43$. She carried $\$ 600$ to the mall. What amount is she left with after shopping in the mall?

Solution: 

Cynthia buys a number of things for the Christmas.  

Cost of the Christmas cake bought = $\$ 150$

Cost of the Christmas tree bought = $\$ 275$

Cost of the chocolates bought = $\$ 78$

Cost of the bouquet of flowers bought = $\$ 43$

Total cost of things bought which is Cynthia’s expenditure = $\$ 150 + \$ 275 + \$ 78 + \$ 43$ = $\$ 546$

Amount carried by Cynthia to the mall for Christmas shopping = $\$ 600$

  The amount which is remaining with her is the difference between the amount with her initially and the amount spent by her. So, the 

Amount left after shopping in the mall = Amount carried to the mall - Amount spent on buying Christmas gifts

Amount left after shopping in the mall = $\$ 600 - \$ 546$

Amount left after shopping in the mall = $ \$ 54$

Thus, the amount left with Cynthia that remains unspent at the mall after doing Christmas shopping is $ \$ 54$.
Example 2: 

Nicholas has $1$ quarter and $2$ pennies. He gets his pocket money from his mother of amount $3$ dimes, $3$ nickels and $4$ pennies. How much money does he have with him now?

Solution: 

Nicholas had some amount with him initially before he gets some more in the source of pocket money from his mother. The amount with him and the amount received are of different denominations. The different denominations given in the problem is quarter, pennies, dimes and nickels. Let us convert all of them into a single denomination that is pennies. This is done for easier calculation. The conversion is as follows:

$1$ quarter = $25$ pennies

$1$ dime = $10$ pennies. So, $3$ dimes = $3 \times 10$ = $30$ pennies

$1$ nickel = $5$ pennies. So, $3$ nickels = $3 \times 5$ = $15$ pennies

Nicholas had $1$ quarter and $2$ pennies which if converted into pennies would be $1$ quarter + $2$ pennies = $25$ pennies + $2$ pennies = $27$ pennies

The pocket money that Nicholas received from his mother if converted to pennies would be $3$ dimes + $3$ nickels + $4$  pennies = $30$ pennies + $15$ pennies + $4$ pennies = $49$ pennies

Total money accumulated is equal to the money he had with him and the money that he received in the form of pocket money from his mother. Thus, total money that Nicholas has with him now = Money owned by him + Pocket money from his mother

Total money that Nicholas has with him now = $27$ pennies + $49$ pennies

Total money that Nicholas has with him now = $76$ pennies
Example 3: 

Gary buys stationery for his school project. He buys $2$ pencils worth $50$ cents each, $3$ erasers worth $20$ cents each, colored pencil box worth $ \$ 2$, red, blue and green colored chart papers each costing $25$ cents, fevi stick worth $10$ cents, scissor worth $ \$3$. What is the amount of the bill he had to pay to buy the stationery

Solution: 

Gray needed stationery for his school project and buys the necessities. The amount that he pays for each of the heads of the stationery is as follows:

Each pencil that he buys costs him $50$ cents. So, when he buys $2$ pencils the amount he had to pay for the pencils is $50 \times 2$ = $100$ cents

Each eraser that he buys costs him $20$ cents. So, when he buys $3$ erasers the amount he had to pay for the erasers is $20 \times 3$ = $60$ cents

Price of one colored pencil box = $ \$ 2$

Each chart paper that he buys be of either red or blue or green in color are all of equal price and costs him $25$ cents. So, when he buys $3$ colored chart papers the amount he had to pay for the chart papers of three different color is $25 \times 3$ = $75$ cents

Price of one fevi stick = $10$ cents

Price of one scissor = $ \$ 2$

Total cost of the stationery bought by Gary for his school project = cost of pencils + cost of eraser + cost of one colored pencil box + cost of red, blue and green chart papers + cost of one fevi stick + cost of one scissor

Total cost of the stationery bought by Gary for his school project = $100$ cents + $60$ cents + $ \$ 2 + 75$ cents + $10$ cents + $ \$ 2$

Total cost of the stationery bought by Gary for his school project = $ \$ 4245$cents

Applying the conversion from cents to dollars, $100$ cents = $ \$ 1\ \Rightarrow\ 245$ cents = $ \$2.45$ cents, we get

Total cost of the stationery bought by Gary for his school project = $ \$ 4 + \$ 245$  cents

Total cost of the stationery bought by Gary for his school project = $ \$ 6.45$ cents

The amount of the bill Gary had to pay to buy the stationery is  $6$ dollars and $45$ cents
Example 4: 

Aarav is buying $5$ packs of gum that cost $ \$ 1.50$ each. He wants to share his gum with two friends. He asks his friends to pay him for their share. Including Aarav, how much does each person spend on gum?

Solution: 

The cost of each gum pack that Aarav buys is $ \$ 1.50$. He buys $5$ packs costing him $5 \times 1.50$ = $ \$7.50$

The number of gums that he buys is then distributed among his two friends including him. The price that he paid for the 

pack of gums is shared between his two friends and he himself. So, total number of heads to be counted who shared the 

cost is $2$ + $1$ = $3$. If $3$ persons paid $ \$7.50$ for the $5$ pack of gums, then the amount which each person paid for the pack 

of gums is $ \$$ $\frac{7.50 }{3}$ = $ \$2.50$.

Thus, the amount each person spend on the gum is $ \$2.50$
Example 5: 

At the end of the week Rima decided to open her piggy bank and count the amount she collected for a week. On counting the coins that was there in the piggy bank she found the amount to be $ \$6.60$ and the number of coins to be $66$. The coins were of different denominations consisting of dimes, nickels and quarters. The relation between the different denominations is such that there are three times as many nickels as quarters and one – half as many dimes as nickels. Find out the number of coins of each kind that is present in the piggy bank. Also, verify the answer using the amount given.

Solution:

We first assume one of the kinds of coin to be a variable and then convert the rest of the kind of coins into it. Let us choose that kind of coin in which other kinds could be converted easily and would also simplify the working of the problem. Nickels are defined in terms of quarters and dimes are defined as nickels, so we’ll assume a variable to represent the number of quarters and then work from there.

Let the number of quarters be $x$. Number of nickels given is thrice the number of quarters, so the number of nickels would be $3x$. Number of dimes given is one – half the number of nickels, so the number of dimes would be $\frac{1}{ 2}$ $\times\ 3x$ = $\frac{3x }{ 2}$. 

Total number of coins = $66$

Number of nickels + number of dimes + number of quarters = $66$

$3x\ +$  $\frac{3x} { 2}$ $+\ x$ = $66$

$4x\ +$  $\frac{3x }{ 2}$ = $66$

Taking the least common denominator to be $2$,

$\frac{8x} {2}$ + $\frac{3x }{ 2}$ = $66$

$\frac{11x}{2}$ = $66$

Multiplying both sides with $2$,

$\frac{11x}{2}$ $\times\ 2$ = $66\ \times\ 2$

$11x$ = $132$

Dividing both sides by $11$,

$\frac{11x}{11}$ = $\frac{132}{11}$

$X$ = $12$

So, the number of quarters = $12$, number of dimes = $\frac{3x} {2}$ = $3\ \times$ $\frac{12 }{2}$ = $18$ and number of nickels = $3x$ = $3\ \times\ 12$ = $36$

Verification: We can verify by counting the total amount present in the piggy bank. If the total amount collected in the piggy bank adds up to $ \$6.60$ then it would be verified that the number of coins of different denominations found is correct.

$1$ quarter = $25$ cents $\Rightarrow\ 12$ quarters = $12\ \times\ 25$ = $300$ cents

$1$ dime = $10$ cents $\Rightarrow\ 18$ dimes = $18\ \times\ 10$ = $180$ cents

$1$ nickel = $5$ cents $\Rightarrow\ 36$ nickels = $36\ \times\ 5$ = $180$ cents

Total amount = $300$ cents + $180$ cents + $180$ cents

Total amount = $660$ cents

Total amount = $6$ dollars and $60$ cents which is equal to the money present in the piggy back as given in the problem. Hence, verified.
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