Help w/ word problem regarding coin quantities: Jessica has 16 dimes and quarters.

seattledude

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Jan 28, 2018
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The problem is this:

Jessica has 16 dimes and quarters. Whitney has twice as many dimes and 1/3 as many quarters as Jessica. If they both have the same amount of money, what coins does each have?

I've tried using a chart and systems of equations to solve but can't figure it out. The solution is this:

Jessica has 10 dimes and 6 quarters
Whitney has 20 dimes and 2 quarters

Can someone show me the proper steps to arriving at this solution? Thanks!
 

mmm4444bot

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… Jessica has 16 dimes and quarters. Whitney has twice as many dimes and 1/3 as many quarters as Jessica. If they both have the same amount of money, what coins does each have?

I've tried using a chart and systems of equations to solve but can't figure it out …
Hi. Please show us the equations that you came up with, even if you think they are wrong. Sometimes, when a student reads a statement like, "Whitney has twice as many dimes as Jessica", they put the factor 2 on the wrong side of the equation (common mistake). We'd like to check over what you've tried so far. Maybe it's just a simple mistake, somewhere.

Please also be sure to read the forum's guidelines. Thanks. :cool:
 
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seattledude

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Jan 28, 2018
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So, here was my original approach

Let d represent the quantity of dimes.
Let q represent the quantity of quarters.

Jessica: d + q = 16
Whitney: 2d + 1/3q = ?

We know that both people have the same amount of money. Consequently,

d + q = 2d + 1/3q

Given that we have d + q = 16, I transformed the equation like so: q = 16 - d. Next, I swapped instances of q for 16 - d like so:

d + (16-d) = 2d + 1/3(16-d)

This did not yield the results I expected. Looking for a correct approach. Thanks.
 

Dr.Peterson

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Nov 12, 2017
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So, here was my original approach

Let d represent the quantity of dimes.
Let q represent the quantity of quarters.

Jessica: d + q = 16
Whitney: 2d + 1/3q = ?

We know that both people have the same amount of money. Consequently,

d + q = 2d + 1/3q

Given that we have d + q = 16, I transformed the equation like so: q = 16 - d. Next, I swapped instances of q for 16 - d like so:

d + (16-d) = 2d + 1/3(16-d)

This did not yield the results I expected. Looking for a correct approach. Thanks.
You actually have a good start. We can work with it.

You've defined (without explicitly stating it, which is an important thing to do):
d = number of dimes Jessica has
q = number of quarters Jessica has

Then you correctly wrote an equation saying Jessica has 16 coins: d + q = 16.

You also wrote an expression for the number of coins Whitney has: 2d + 1/3q. This depends on the facts
2d = number of dimes Whitney has
(1/3)q = number of quarters Whitney has

These are correct facts. But we don't know anything about the number of coins Whitney has; what we know is that they both have the same AMOUNT OF MONEY -- that is, the same VALUE.

Write an expression for the VALUE of each one's coins, and set those expressions equal. That will give you the second equation you need.
 
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