Answer:
5. He rented 7 new releases videos
6. 4 3-bedrooms units.
7. length: 37, width: 18
8. 81 dimes, 47 quarters
Explanation:
5. Videos
X: New releases
Y: Regular titles
EQ1: x + y = 18 (he rented 18 videos)
EQ2: 3x + 2y = 43 (he paid $43 for the 18 videos)
By EQ1, we can isolate y-value as y = 18 - x
We place this y-value into EQ2:
3x + 2(18 - x) = 43 and we solve:
3x + 36 - 2x = 43
3x - 2x = 43 - 36
x = 7
He rented 7 new releases videos
6. bedroom units
X: 2-bedrooms units
Y: 3-bedrooms units
EQ1: x + y = 7 (they have 7 units)
EQ2: 450x + 650y = 3950 (their monthly renting revenues)
By EQ1, we can isolate x as x = 7 - y (since we're looking for 3-bedrooms units), and place that value in EQ2:
450 (7 - y) + 650y = 3950
3150 - 450y + 650y = 3950
200y = 800
y = 4
So, they have 4 3-bedrooms units.
7. Rectangle
X: length
Y: width
EQ1: x + y = 55 (since perimeter is 110 and includes 2x + 2y)
EQ2: x = 2y + 1 (length is twice the with, plus 1)
Since we are asked to find both values, it doesn't matter by which we begin. By EQ1, we can do x = 55 -y, and place that value in EQ2, to get:
55 - y = 2y + 1
54 = 3y
y = 18
Place y = 18 in EQ1 to find x:
x + 18 = 55
x = 37
8. Dimes and quarters
X: dimes
Y: quarters
EQ1: x = y + 34 (34 more dimes than quarters)
EQ2: 10x + 25y = 1985 (total value of the collection)
Let's place the value of x from EQ1 in EQ2:
10 (y + 34) + 25y = 1985
10y + 340 + 25y = 1985
35y = 1645
y = 47
From EQ1, we then have
x = 47 + 34 = 81
So, we have 81 dimes ($8.10) and 47 quarters ($11.75), for a total of $19.85.