A jar contains 40 coins consisting of dimes and quarters and having a total value of $4.90. How many of each kind of coin are there?

Livia Cardenas

Livia Cardenas

Answered question

2022-07-30

A jar contains 40 coins consisting of dimes and quarters and having a total value of $4.90. How many of each kind of coin are there?

Answer & Explanation

Ragazzonibw

Ragazzonibw

Beginner2022-07-31Added 15 answers

We need two sets of equation
eq #1- represent the number of coins
d=dimes
q = quarters
40= d + q
Eq#2 Values of the coins
4.90 = 0.10d + 0.25 q
from equation 1, let us find an expression for the quarters.
so;
q = 40-d
*Lets substitute this equation in eq # 2
4.9 = 0.10d + 0.25(40 -d)
*simplifying
4.9=0.10d + 10 - 0.25d
4.9-10 = 0.10d - 0.25d
-5.1 = -0.15 d ==>
d= 34 coins
So substitute the number of dimes in eq1
40=d+q
40=34+q
q=6
6 quarters, 34 dimes
Francisco Proctor

Francisco Proctor

Beginner2022-08-01Added 6 answers

Total no. of dimes and quarters = 40
let , x = no. ofdimes; so total value of dimes = x *1/10 = x/10 $
hence, (40 - x) = no. of quarters ; so total value ofquarters = (40 - x)*1/4 = (40 - x)/4 $
total value of dimes and quarters = 4.90 $
hence we can form an equation like,
x / 10 + (40 - x)/4 = 4.9
=> x/10 + 10 - x /4 = 4.9
=> x/4 - x /10 = 10 - 4.9
=> (5x - 2x)/20 = 5.1
=> 3x / 20 = 5.1
=> x = 5.1 * 20 / 3
= 34
hence no. of dimes = x = 34
no. of quarters = 40 - x = 40 - 34 = 6
Answer:
no. of dimes =34
no. of quarters = 6

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?