three times as many dimes as nickels and 6 more quarters than dimes. Total in change is 5.90 , how many nickels, dimes and quarters does she have?

Question

Madison has three times as many dimes as nickels and 6 more quarters than dimes in her change purse. If Madison has 5.90 in change, how many nickels, dimes and quarters does she have?

Answer 1

Diane,  I totally concur with Catherine on this solution !  If you have difficulty with decimals, just express all of the parts in pennies !!!!   Your equation would look like this :   5(X) + 10( 3X ) + 25 ( 3X + 6 ) = 590  cents  You still have to use the values as multipliers, because the equation can only make "sense"  if you have    cents =  cents    on both sides !

You simplify both sides to get   110 X   +  150  =  590 ;   then,   110 X  =  440  by subtraction.  Here's another thing to consider:   If your last division does NOT equal a whole number, then you made a multiplication mistake or an addition error......just check your math and the error will be uncovered.  This is the difficult part of word problems that students find frustrating!!!  Just double-check your work.  Good luck Monday, and get back to one of us again, if you need more help!

 

Charles S

Hendersonville, NC.

 

Answer 2

Let x equal the number of nickels. Therefore, 3x is the number of dimes, and (3x+6) is the number of quarters. 

 

.05x is the total amount of money in nickels; .10(3x) is the total money in dimes; .25(3x +6) is the total money in quarters. The total amount of all the change is given as 5,90.

 

So set up this equation and solve for x: .05x + .10(3x) + .25(3x+6) = 5.90

 

.05x +.30x + .75x +1.50 = 5.90      

 

Subtract 1.50 from both sides and complete addition on left to arrive at:  1.10x = 4.40

 

Divide both sides by 1.10 to solve for x:   x = 4

 

Substitute 4 for x in original equation:   .20 + 1.20 + 3.00 + 1.50 = 5.90