the total amount in pesos of 30 coins consisting of 5-peso coin and 10-peso coin is php 215 . how many coins of each type are there?
if there were x 5-peso coins, then the rest (30-x) are 10-pesos. Adding up the value, you get
5x + 10(30-x) = 215
now solve for x
5x+10(30-x)=215
5x+300-10x =215
5x-10x=215-300
-5x/5 = -85/5
x= 17
Let's solve this step-by-step:
Step 1: Assign variables.
Let's call the number of 5-peso coins "x" and the number of 10-peso coins "y".
Step 2: Create equations.
We know that the total number of coins is 30, so
x + y = 30 ...(Equation 1)
We also know that the total amount of money is Php 215, so we can create another equation with the values of the coins:
5x + 10y = 215 ...(Equation 2)
Step 3: Solve the equations.
We can solve the system of equations (Equation 1 and Equation 2) to find the values of x and y.
From Equation 1, we can isolate x:
x = 30 - y
Now substitute the value of x in Equation 2:
5(30 - y) + 10y = 215
Simplify and solve for y:
150 - 5y + 10y = 215
5y = 65
y = 13
Now substitute the value of y back into Equation 1 to find x:
x + 13 = 30
x = 30 - 13
x = 17
Step 4: Answer the question.
There are 17 coins with a denomination of 5 pesos and 13 coins with a denomination of 10 pesos.
To determine the number of coins of each type, we can set up a system of equations. Let's represent the number of 5-peso coins as "x" and the number of 10-peso coins as "y."
From the given information, we know that there are a total of 30 coins. Therefore, we can write the equation:
x + y = 30 -- Equation (1)
We also know that the total value of these coins in pesos is PHP 215. The value of each 5-peso coin is 5 pesos, and the value of each 10-peso coin is 10 pesos. So, the value equation is:
5x + 10y = 215 -- Equation (2)
Now, we have a system of two equations (Equation 1 and Equation 2) that we can solve simultaneously. Let's solve this system of equations using the substitution method:
Step 1: Solve Equation (1) for x:
x = 30 - y
Step 2: Substitute the value of x in Equation (2):
5(30 - y) + 10y = 215
Step 3: Simplify and solve for y:
150 - 5y + 10y = 215
5y = 215 - 150
5y = 65
y = 65/5
y = 13
Step 4: Substitute the value of y back into Equation (1) to find x:
x + 13 = 30
x = 30 - 13
x = 17
Therefore, there are 17 coins with a denomination of 5 pesos and 13 coins with a denomination of 10 pesos.