V. Solve the following problems. Show your solution.
1. Ronaldo took a handful of change out of his pocket and noticed that he was only holding five-peso coin and ten-peso coin in his hand. He counted and found that he had 21 coins that amounted to Php. 180.00 How many five-peso and ten-peso coins does Ronaldo have?
2. Anne wants to put a ribbon around her bed that is twice as long as its width. She uses 36 feet of ribbon. What are the dimensions of the bed?
3. 500 tickets are sold for a concert: lower box seats for Php. 1.200.00 each and upper box seats for Php. 800.00 each. If the total box office take is Php. 480,000,00, how many of each kind of ticket were sold?
4. Two prime numbers have a product of 221. What are the numbers?
5. The square of a certain positive number is six more than five times the a number. What is the number?
1. Ronaldo took a handful of change out of his pocket and noticed that he was only holding five-peso coin and ten-peso coin in his hand. He counted and found that he had 21 coins that amounted to Php. 180.00 How many five-peso and ten-peso coins does Ronaldo have?
2. Anne wants to put a ribbon around her bed that is twice as long as its width. She uses 36 feet of ribbon. What are the dimensions of the bed?
3. 500 tickets are sold for a concert: lower box seats for Php. 1.200.00 each and upper box seats for Php. 800.00 each. If the total box office take is Php. 480,000,00, how many of each kind of ticket were sold?
4. Two prime numbers have a product of 221. What are the numbers?
5. The square of a certain positive number is six more than five times the a number. What is the number?
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Answer:
1.
Let
x = # of pcs of P5 coins
y = # of pcs of P10 coins
Conditions:
x + y = 21 ===> combination # of pcs of total coins
so we can also say:
x = 21 - y
or
y = 21 - x
We know that the total amount of combination of coins amount to P180.00
so we can say that,
5x + 10y = 180
but
y = 21 - x (or use x = 21 - y)
so,
5x + 10(21 - x) = 180
5x + 210 - 10x = 180
-5x = 180 - 210
-5x = -30
x = -30/-5
x = 6
solve for y,
y = 21 - x
y = 21 - 6
y = 15
Therefore there are 6 pcs. P5 coins and 15 pcs. P10 coins.
Check Answer:
(6 x P5) + (15 x P10) = P180
P30 + P150 = P180
P180 = P180 ✓✓✓ True
2.L=24 W=12
1+2=3
36÷3=12
12
X=12
3.the total tickets were sold is 20,056
4.13 and 17
221 is: a product of two prime numbers, 13 and 17, making it a semiprime. the sum of five consecutive prime numbers (37 + 41 + 43 + 47 + 53) the sum of nine consecutive prime numbers (11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 + 41)
5.
Step-by-step explanation: