*I NEED THESE IN ALGEBRAIC EXPRESSIONS!
1.) The larger of two numbers is 1 less than 3 times the smaller. Their sum is 63. Find the numbers.
2.) Find two numbers whose sum is 92, if the first is 4 more than 7 times the second.
3.) The sum of two numbers is 172. The first is 8 less than 5 times the second. Find the first number.
4.)Together, a necklace and a bracelet cost $192. Find the price of each if the necklace costs 3 times as much as the bracelet.
5.) Grandpa's age is 6 years less than 6 times Junior's age. The sum of their ages is 78. Find each of their ages.
6.) The first of two films laster 3 minutes less than then twice as long as the second. Together the two films laster 132 minutes. How long was the first film?
1. 2nd number = x,
1st number = (3x - 1).
x + (3x - 1) = 63,
4x -1 = 63,
4x = 64,
x = 16.
2. 2nd number = x,
1st number = (7x + 4),
x + (7x + 4) = 92,
8x + 4 = 92,
8x = 92 - 4,
8x = 88,
x = 11.
The remaining problems are similar.
Sure! Let's express each of the given problems in terms of algebraic expressions.
1.) Let's assume the smaller number as 'x' and the larger number as 'y'.
According to the problem, the larger number is 1 less than 3 times the smaller number, so we can write the equation as:
y = 3x - 1
The sum of the two numbers is 63, so we can write another equation:
x + y = 63
Now we have a system of equations that can be solved simultaneously to find the values of x and y.
2.) Let's assume the second number as 'x' and the first number as 'y'.
According to the problem, the first number is 4 more than 7 times the second number, so we can write the equation as:
y = 7x + 4
The sum of the two numbers is 92, so we can write another equation:
x + y = 92
Again, we have a system of equations that can be solved simultaneously to find the values of x and y.
3.) Assume the second number as 'x' and the first number as 'y'.
According to the problem, the first number is 8 less than 5 times the second number, so we can write the equation as:
y = 5x - 8
The sum of the two numbers is 172, so we can write another equation:
x + y = 172
Once more, we have a system of equations that can be solved simultaneously to find the values of x and y.
4.) Assume the price of the bracelet as 'x' and the price of the necklace as 'y'.
According to the problem, the necklace costs 3 times as much as the bracelet, so we can write the equation as:
y = 3x
The total cost of the necklace and bracelet is $192, so we can write another equation:
x + y = 192
Now we have a system of equations that can be solved simultaneously to find the values of x and y.
5.) Assume Junior's age as 'x' and Grandpa's age as 'y'.
According to the problem, Grandpa's age is 6 years less than 6 times Junior's age, so we can write the equation as:
y = 6x - 6
The sum of their ages is 78, so we can write another equation:
x + y = 78
Again, we have a system of equations that can be solved simultaneously to find the values of x and y.
6.) Assume the length of the second film as 'x' and the length of the first film as 'y'.
According to the problem, the first film lasted 3 minutes less than twice as long as the second film, so we can write the equation as:
y = 2x - 3
Together, the two films lasted 132 minutes, so we can write another equation:
x + y = 132
Once again, we have a system of equations that can be solved simultaneously to find the values of x and y.