lly gave her brother $3.95 in quarters and dimes. If the number of quarters is 6 more than the number of dimes, how many quarters did Sally give her brother

Question

sally gave her brother $3.95 in quarters and dimes. If the number of quarters is 6 more than the number of dimes, how many quarters did Sally give her brother?
Sally gave her brother quarters.
NextReset

Answer 1

Good Morning, Alex,

When working this problem, I always recommend to my students that they convert the sum - which in your case in $3.95 to cents. This simplifies matters as you will see. 

According to the information given in the problem: 

10(n_d)+ 25(n_q) ₌ 395   

n equals the number, _d equals the number of dimes, and _q equals the number of quarters. The value of 10 i s assigned due to a dime equaling 10 cents, and 25 is assigned due to a quarter being equal to 25 cents. 


You also know from the information given the following: 

n_{q =} n_d + 6  "the number of quarters is six more than the number of dimes. Again, n equals the number. 

Therefore, you can now substitute the above wherever you see n_q  Therefore: 

10(n_d) + 25(n_d + 6) = 395   

Now, we can simplify, right> 

10(n_d) + 25n_d + 150 = 395   Due to the distributive property. 

10n_d + 25n_d = 245                Subtracting 150 from both sides.

35n_d = 245 

n_d = 7                                  Number of dimes equals 7

Remember n_q = n_d + 6

Therefore: n_q = 7 + 6 

Or, 

n_q = 13

Checking our work by totaling the coins:  

7 * 10 = 70 (There are 10 cents in a dime)

13 * 25 = 325 (There are 25 cents in a quarter).

Added together the two above values of .70 and 3.25 do in fact, equal $3.95. 

I hope I have helped you and that you have a great weekend. Please let me know if this answer makes sense by following up on the comment section below. Have a great day. Best!