can anyone solve these, math problem?

Question

1) xavier bought 5 red delicious apples and 4 granny smith apples at a cost of $4.81. Dean bought one of each of the two types at a cost of $1.08. find the cost for each kind of apple.

2) four single-sided disks and two double sided disks cost a total of $5.10. Two single sided and four double sided disks cost $5.40. Find the unit cost for each.

3) the perimeter of an isosceles triangle is 37inches. the lengths of the two equal legs are 6in less then 3 times the length of the base. Find the lengths of the three sides.

Answer 1

5x + 4y = 4.81
x + y = 1.08
so, red delicious = $0.52 a,d granny = $0.95

4s + 2d = 5.10
2s + 4d = 5.40
so, single = $0.80 and double =$0.95

b+ 2l = 37
3b = l - 6
so, base = 3.57 and each leg is 16.71

Answer 2

1. Red Delicious = X. Granny Smith = Y.
Use two equations and substitute one in the other, i.e.
Xavier -> 5X + 4Y = 4.81. Dean -> 1X + 1Y = 1.08.
1x = 1.08 - 1Y, then substitute into Xavier.
5X + 4(1.08 - 1X) = 4.81, then 5X + 4.32 - 4X = 4.81,
then 5x - 4X = 4.81 - 4.32, then X = .49 (Cost of Red Delicious)
Now substitute the value of X back into either equation.
(5 * .49) + 4Y = 4.81 --> 2.45 + 4Y = 4.81 --> 4Y = 2.36 _> Y = .59 (Cost of Granny Smith)

2. Use the same process of substitution..
4X (double-sided) + 2Y (single-sided) = $5.10
2X + 4Y = $5.40 --> same as X + 2Y = 2.70
X = 2.70 - 2Y Then substitute with just one variable
4 (2.70 - 2Y) + 2Y = 5.10 --> 10.80 - 8Y + 2Y = 5.10
10.80 - 6Y = 5.10 --> 10.80 - 5.10 = 6Y -->
5.70 = 6Y --> .95 = Y (Cost of Double-sided)
Substitute into X + 2Y = 2.70 --> X + 2(.95) = 2.70
X = 2.70 - 1.90 = .80 (Cost of Single-sided)

3. Still use the substitution and reduction to a single variable.
Isosceles is a right triangle with two equal sides at 90 degrees.
37 = 2X (equal sides) + Y (base) --> y = 37 - 2X.
The verbiage here could mean the total length of the two equal sides (2X) or the length of a single side (1X). I've chosen 2X.
Other equation = 2X (equal sides) = 3Y (3 * base length) - 6
Substitute to reduce to one variable.
2X = 3 ( 37-2X) - 6 --> 2X = 111 - 6X - 6
8X = 105 --> X = 13.125.
Two sides = 13.125 each = 26.5. 37 - 26.5 = 10.5 = Base.

Answer 3

1) lets take x=red delicious apples
y=granny smith

5x+4y=4.81
x+y=1.08

multiply the second eqn by 4

4x+4y=4.32

1st eqn minus 2nd eqn

x=0.49

and since x+y=1.08
y=1.08-0.49=0.59


2) lets take x=single, y=double

4x+2y=5.10
2x+4y=5.40

add both eqn together

6x+6y=10.50

divide this by 3

2x+2y=3.50

take 1st eqn minus this eqn

2x=1.60
x=0.80

sub back into 2x+2y=3.50
2(0.80)+2y=3.50
1.60+2y=3.50
2y=3.50-1.60
=1.90
y=0.95


3)lets take x=base,y=one of the equal legs

x+2y=37
y=3x-6(length of the 2 equal legs are 6in less than thrice the base)

sub y=3x-6 into the 1st eqn
x+2(3x-6)=37
7x-12=37
7x=37+12
7x=49
x=7
y=3(7)-6=21-6=15

Answer 4

1)5x+4y=4.81
x+y=1.08

5x+4y=4.81
-4x-4y=-4.32
==========
x=.49

5(.49)+4y=4.81
4y=4.81-2.45
4y=2.36
y=.59

The costs of each apple are 0.59 and 0.49

2)4s+2d=5.10
2s+4d=5.40

4s+2d=5.10
-4s-8d=-10.80
===========
-6d=-5.70
d=.95

2s+4(.95)=5.40
2s=5.40-3.80
2s=1.60
s=.80

The cost of single-sided disks are 0.80 and the costs of double-sided disks are 0.95.

3)2l+b=37
3b=l-6

b=(1/3)l-2
2l+(1/3)l-2=37
(6/3)l+(1/3)l-2=37
(6/3)l+(1/3)l=39
7/3l=39
l=117/7=16.71

3b=16.71-6
3b=10.71
b=3.57

The lengths are 16.71 in. and the base is 3.57 in.

Answer 5

All are solved as simultaneous equations. I'll do one for you. You should be able to solve the other two.

5R + 4G = 4.81
1R + 1G = 1.08

if 1R + 1G = 1.08, then 4R+4G = 4.32 (mult each term by 4)
subtract the second from the first:

5R + 4G = 4.81
4R + 4G = 4.32
----------------------
1R = .49 so a red delicious is 49 cents
1R + 1G = 1.08 so a granny smith is 59 cents