Math CentralQuandaries & Queries


Question from Renae, a student:

Charity has 42 more pennies than dimes. Hope has 7 times as many pennies than dimes. Hope and Charity have the same number of dimes. Together they have $5.46. How many dimes and pennies do each have?

Hi Renae,

Charity and Hope each have the same number of dimes so let $d$ be the number of dimes that each of them has. I want to concentrate on Charity.


Coins Number of coins Value of coins in cents
dimes $d$ $10 \;d$
pennies $d + 42$ $d + 42$

Thus the total value of Charity's coins in cents is $10\;d + d + 42.$

What is the total value of Hope's coins in cents? Together the value of their coins is $546$ cents. Solve for $d.$



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