Question

12 chris made at least one error as she found the value of this expression. $2(-20) + 3\left\frac{5}{4}(-20)\
ight + 5\left\frac{2}{5}(50)\
ight + 4(50)$ step 1: $2(-20) + 3(-25) + 5(20) + 4(50)$ step 2: $(3 + 2)(-20 + -25) + (5 + 4)(20 + 50)$ step 3: $5(-45) + 9(70)$ step 4: $-225 + 630$ step 5: $405$

Explanation:

Step1: Calculate initial bracket values

$2(-20) = -40$, $\frac{5}{4}(-20) = -25$, $\frac{2}{5}(50)=20$, $4(50)=200$
Updated expression: $-40 + 3(-25) + 5(20) + 200$

Step2: Resolve remaining multiplications

$3(-25)=-75$, $5(20)=100$
Updated expression: $-40 -75 + 100 + 200$

Step3: Add/subtract left to right

$-40 -75 = -115$; $-115 + 100 = -15$; $-15 + 200 = 185$

Step4: Identify Chris's error

Chris incorrectly grouped terms in Step2: she tried to factor non-like terms, violating order of operations. Terms cannot be grouped as $(3+2)(-20 + -25)$ or $(5+4)(20+50)$ because the coefficients multiply different values, not shared terms.

Answer:

Chris's first error occurs in Step 2, where she incorrectly grouped non-like terms instead of following the order of operations. The correct value of the expression is $\boldsymbol{185}$.