The Everton College Store Paid $1660 For An Order Of 44 Calculators. The Store Paid $11 For Each Scientific Calculator. The Others, All Graphing Calculators, Cost The Store $53 Each. How Many Calculator Was Order For Each?
Solve by the elimination method
0.3x-0.2y=4
0.2x+0.3y=-23/19 Find the solution of the system
2. Solve by the elimination method
0.05x+0.25y=66
0.15x+0.05y=72 Find the solution of the system
3. The perimeter of a rectangle is 190 inches. The length exceeds the breadth by 29 inches. Find the length and width.
Answer:
1. Let S be the number of scientific calculators, G be the number of graphing calculators.
S + G = 44 (the store bought 44 calculators)
11S + 53G = 1660 (the total purchase was $1660)
Multiply the first equation by 11 and subtract from the second
(11S+53G) - 11(S+G) = (1660) - 11(44)
42G = 1176
G = 1176/42 = 28
S = 44-28 = 16
The store ordered 16 medical and 28 graphing calculators.
2. Use the elimination methd
.3x - .2y = 4
.2x + .3y = -23/19
Multiply the first equation by 3 and add to 2 times the second equation. This will eliminate y.
3(.3x-.2y) + 2(.2x+.3y) = 3(4) + 2(-23/19)
.9x + .4x = 12 - 46/19
1.3x = (228-46)/19
x = 182/(19*1.3) ≈ 7.3684
y = (.3x-4)/.2 = 1.5x-20 ≈ 1.5(7.3684)-20 = -8.9474
3. Use the ending method
.05x + .25y = 66
.15x + .05y = 72
Multiply the first equation by 3 and subtract the second. This will eliminate x.
3(.05x+.25y) - (.15x+.05y) = 3(66) - 72
.75y - .05y = 198-72
y = 126/.70 = 180
x = (66-.25y)/.05 = 21/.05 = 420
Check: .15(420)+.05(180) = 63+9 = 72
4. P = 190 = 2(w+(w+29))
95 = 2w + 29
66 = 2w
33 inches = width
62 inches = length
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Answer:
1. Let S be the number of scientific calculators, G be the number of graphing calculators.
S + G = 44 (the store bought 44 calculators)
11S + 53G = 1660 (the total purchase was $1660)
Multiply the first equation by 11 and subtract from the second
(11S+53G) - 11(S+G) = (1660) - 11(44)
42G = 1176
G = 1176/42 = 28
S = 44-28 = 16
The store ordered 16 medical and 28 graphing calculators.
2. Use the elimination methd
.3x - .2y = 4
.2x + .3y = -23/19
Multiply the first equation by 3 and add to 2 times the second equation. This will eliminate y.
3(.3x-.2y) + 2(.2x+.3y) = 3(4) + 2(-23/19)
.9x + .4x = 12 - 46/19
1.3x = (228-46)/19
x = 182/(19*1.3) ≈ 7.3684
y = (.3x-4)/.2 = 1.5x-20 ≈ 1.5(7.3684)-20 = -8.9474
3. Use the ending method
.05x + .25y = 66
.15x + .05y = 72
Multiply the first equation by 3 and subtract the second. This will eliminate x.
3(.05x+.25y) - (.15x+.05y) = 3(66) - 72
.75y - .05y = 198-72
y = 126/.70 = 180
x = (66-.25y)/.05 = 21/.05 = 420
Check: .15(420)+.05(180) = 63+9 = 72
4. P = 190 = 2(w+(w+29))
95 = 2w + 29
66 = 2w
33 inches = width
62 inches = length
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