Question 3148: a sum of money amounting to $3.55 consists of dimes and quarters. if there are 25 coins in all, how many quarter are there. how many dimes Answer by WannabeCAgirl83(35) (Show Source):
Step 1
Finding equations:
A sum of money amounting $3.55 consists of dimes and quarters.
0.25x + 0.1y = 3.55 → Eqn 1
If there are 25 coins in all, how many quarters are there, and how many dimes are there?
x + y = 25 → Eqn 2
Step 2
Isolating x in Eqn 2:
x + y = 25 | - y on both sides
x = 25 - y
Step 3
Substituting x in Eqn 1 with the term found for x in step 2. Then isolating y:
0.25x + 0.1y = 3.55
0.25(25 -y) + 0.1y = 3.55
6.25 - 0.25y + 0.1y = 3.55 | re-arranging
6.25 - 0.15y= 3.55 | - 6.25 on both sides
- 0.15y= - 2.7 | : - 0.15 on both sides
y = 18 → There are 18 dimes.
Step 4
Substituting y in Eqn 2 by the value found for y. Then again isolating x:
x + y = 25
x + 18 = 25 | - 18 on both sides
x = 7 → There are 7 quarters.
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