A)One packet of biscuits cost $x and one cup of ice cream $y
B)One packet of biscuits and two cups of ice cream cost $8.00, while three packets of biscuits and one cup ice cream cost $9.00
1) write a pair of simultaneous equations in x and y to represent the given info above
Is the ans = 1x+2y=$8.00
3X+1y=$9.00
How do i find the cost of one biscuit and one cup of ice cream??
Those are the correct equations, but you do not have to write the "1" as a coefficient. In algebra, that just isn't done.
Just solve these two equations:
x + 2y = 8
3x = y = 9
You can rewrite the first equation as
3x + 6y = 24
By subtracting the 2nd eq from the 3rd), you eliminate x and get
5y = 15
Take it from there.
The longest loaf of bread measured 1.405 feet one and three fourths in inches. In length. It was cut into half slices thick. How many slices were there?
You are correct! The pair of simultaneous equations that represents the given information is:
1x + 2y = $8.00 (equation 1)
3x + 1y = $9.00 (equation 2)
To find the cost of one biscuit (x) and one cup of ice cream (y), we can solve the system of equations using any method of solving simultaneous equations. Let's use the substitution method:
From equation 1, we can isolate x:
1x = $8.00 - 2y
x = $8.00 - 2y (equation 3)
Now, substitute the value of x from equation 3 into equation 2:
3($8.00 - 2y) + 1y = $9.00
Simplifying the equation:
$24.00 - 6y + 1y = $9.00
$24.00 - 5y = $9.00
Next, subtract $24.00 from both sides:
-5y = -$15.00
Divide both sides by -5:
y = $3.00
Now, substitute the value of y into equation 3 to find x:
x = $8.00 - 2($3.00)
x = $8.00 - $6.00
x = $2.00
Therefore, the cost of one biscuit (x) is $2.00 and the cost of one cup of ice cream (y) is $3.00.
To find the cost of one biscuit (x) and one cup of ice cream (y), you need to solve the pair of simultaneous equations that represent the given information.
The equations can be written as follows:
Equation 1: 1x + 2y = $8.00
Equation 2: 3x + 1y = $9.00
To solve these equations, you can use either the substitution method or the elimination method. Let's use the elimination method in this case:
Multiply Equation 1 by 3 and Equation 2 by 2 to make the coefficients of y the same in both equations:
Equation 1: 3(1x + 2y) = 3($8.00) which gives us 3x + 6y = $24.00
Equation 2: 2(3x + 1y) = 2($9.00) which gives us 6x + 2y = $18.00
Now, subtract Equation 2 from Equation 1 to eliminate y:
(3x + 6y) - (6x + 2y) = $24.00 - $18.00
Simplifying, we get -3x + 4y = $6.00
Next, solve this new equation for either x or y. Let's solve it for x:
-3x = $6.00 - 4y
Divide both sides by -3:
x = ($6.00 - 4y) / -3
x = (-6.00 + 4y) / 3
Now, substitute this value of x into one of the original equations, say Equation 1:
1((-6.00 + 4y) / 3) + 2y = $8.00
(-6.00 + 4y + 6y) / 3 = $8.00
Multiply both sides by 3 to eliminate the fraction:
-6.00 + 4y + 6y = $24.00
Combine like terms:
10y = $24.00 + $6.00
10y = $30.00
Divide both sides by 10:
y = $3.00
Now that we know the value of y, we can substitute it back into one of the original equations to find x. Let's use Equation 1:
1x + 2($3.00) = $8.00
x + $6.00 = $8.00
Subtract $6.00 from both sides:
x = $8.00 - $6.00
x = $2.00
So, the cost of one biscuit (x) is $2.00, and the cost of one cup of ice cream (y) is $3.00.