$$ 43 \quad $$ Calculate the value of $$ t $$ if $$ 1.5 \times 174=t \times 4.5 \times 87 $$

Question

UpStudy AI · Accepted Answer

We are given the equation

$$
1.5 \times 174 = t \times 4.5 \times 87.
$$

**Step 1. Compute the left-hand side:**

$$
1.5 \times 174 = 261.
$$

**Step 2. Compute the product on the right-hand side (excluding $$ t $$):**

$$
4.5 \times 87 = 391.5.
$$

So the equation becomes

$$
261 = t \times 391.5.
$$

**Step 3. Solve for $$ t $$:**

$$
t = \frac{261}{391.5}.
$$

**Step 4. Simplify the fraction:**

Divide both the numerator and the denominator by 3:

$$
t = \frac{261 \div 3}{391.5 \div 3} = \frac{87}{130.5}.
$$

Next, divide both the numerator and the denominator by 1.5:

$$
t = \frac{87 \div 1.5}{130.5 \div 1.5} = \frac{58}{87}.
$$

Finally, note that $$58 = 2 \times 29$$ and $$87 = 3 \times 29$$, so cancel the common factor $$29$$:

$$
t = \frac{2}{3}.
$$

**Final Answer:**

$$
t = \frac{2}{3}.
$$
$$ t = \frac{2}{3} $$

\( 43 \quad \) Calculate the value of \( t \) if \[ 1.5 \times 174=t \times 4.5 \times 87 \]