When using a number line to model addition, what does the first integer in a subtraction problem tell you?
1 answer:
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With the help of the ratio method, we conclude that 72 grams of sugar should be added.
<h3>What is Ratio Method?</h3>- In the ratio method, we compare two quantities by equating their two ratios; this equation is also referred to as a proportion.
- The cross-multiplication method will be used to solve it.
So, 'n=5' will be the number of rings.
- 'w = 18 grams' will be the weight of each ring.
- Total weight: w₀ = n × w = 5 × 18 = 90 grams
Let 's' be silver. Then,
- New weight: wₙ = s + 90
- Old % of gold: p₀ = 90% = 0.9
- New % of gold: pₙ = 50% = 0.5
Now, use the ratio method as follows:
- 90 × 0.9 = 0.5 × (s + 90)
- 81 = 0.5s + 0.5 × 90
- 81 = 0.5s + 45
- 81 - 45 = 0.5s
- 36 = 0.5s
- 36/0.5 = s
- 72 = s
- So, s = 72
Therefore, with the help of the ratio method, we conclude that 72 grams of sugar should be added.
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The correct question is given below:
A jeweler has five rings, each weighing 18 grams, made of alloys of 10% silver and 90% gold. He decides to melt down the rings and add enough silver to reduce the gold content to 50%. How much silver should he add?
Answer:
<u>Option B. sin(s) = cos(u)</u>
Step-by-step explanation:
The rest of the question is the attached figure.
Complementary angles - two angles that add to 90 degrees.
The sine of one of them will be equal to the cosine of other angle.
For the attached figure:
The set all complementary angles are:
- angle s and angle t
- angle u and angle v
- angle s and angle u
- angle t and angle v
We will check the options:
A. sin(t) = sin(u) ⇒(<u>wrong</u>) because t and u are not complementary angles
B. sin(s) = cos(u) ⇒ (<u>True</u>) ⇒ s and u are complementary angles and sine of one of them will be equal to the cosine of other angle.
C. cos(s) = sin(v) ⇒(<u>wrong</u>) because t and u are not complementary angles
D. cos(t) = cos(v) ⇒(<u>wrong</u>) because t and v are complementary angles but sine of one of them should be equal to the cosine of other angle.
<u>The answer is option B. sin(s) = cos(u)</u>
