Lizzie has 18 dimes and 12 quarters
<em><u>Solution:</u></em>
Let "d" be the number of dimes
Let "q" be the number of quarters
We know that,
value of 1 dime = $ 0.10
value of 1 quarter = $ 0.25
Given that LIzzie has 30 coins
number of dimes + number of quarters = 30
d + q = 30 ---- eqn 1
Also given that the coins total $ 4.80
number of dimes x value of 1 dime + number of quarters x value of 1 quarter = 4.80
0.1d + 0.25q = 4.8 ------ eqn 2
Let us solve eqn 1 and eqn 2
From eqn 1,
d = 30 - q ---- eqn 3
Substitute eqn 3 in eqn 2
0.1(30 - q) + 0.25q = 4.8
3 - 0.1q + 0.25q = 4.8
0.15q = 1.8
<h3>q = 12</h3>
From eqn 3,
d = 30 - 12
<h3>d = 18</h3>
Thus she has 18 dimes and 12 quarters
Two figures that have the same shape are said to be similar. When two figures are similar, the ratios of the lengths of their corresponding sides are equal. To determine if the triangles below are similar, compare their corresponding sides.
Answer :
1
Step-by-step-explanation :
Given,
Diameter of the can = 3"
Height of the can = 7"
Looking at how the cans are arranged in the box, that is 4 x 5 (4 rows of cans [width] with 5 cans in each row [length])
The length of the box (L) = 5 cans multiplied by each can's diameter = 5 × 3" = 15"
The width of the box (W) = 4 cans multiplied by each can's diameter) = 4 × 3" = 12"
The height of the box (H) = 2 layers of cans = 2 cans multiplied by each can's height = 2 × 7" = 14"
Therefore, the volume of the box = Length (L) × Width (W) × Height (H) = 15" × 12" × 14" = 2520 inches³
Volume of the box = 2520 inches³
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There is also an alternative method to calculate the volume of the box:
Consider each can. Although the can is cylindrical, each can would occupy the space required by a cuboid.
So, for each Cuboid space, the diameter of the can will be the length and width of the cuboid and the height of the can will be the height of the cuboid.
Therefore, for each can,
Length (L) = 3"
Width (W) = 3"
Height (H) = 7"
Volume occupied by one can (that is a cuboid) = L × W × H = 3" × 3" ×7" = 63 inches³
There are 40 such cans in total inside the box; therefore,
Volume of the box = 40 × 63 inches³ = 2520 inches³
